Trajectory proximity lookup method, device, electronic device, and readable storage medium

Abstract

The present disclosure provides a trajectory proximity lookup method, apparatus, electronic device, and readable storage medium, and relates to the field of computer technology. The trajectory proximity lookup method includes the steps of acquiring a first trajectory of a lookup target and determining spatial location information of the first trajectory; generating a trajectory signature according to the positional relationship between the spatial location information of the first trajectory and the lookup target area; determining a spatial location index code of the first trajectory through XZ-Ordering; and constructing a spatial range index of the first trajectory based on the trajectory signature and the spatial location index code. According to the technical details of the present disclosure, the computational amount of time complexity of the trajectory proximity lookup process is reduced, the efficiency of indexing and lookup is increased, and the overhead of disk reading and writing and verification calculations is reduced.

Description

Technology Field

[0001] The present disclosure claims priority to the Chinese patent application filed on December 28, 2020, with application number 202011583540.9, titled "Method, apparatus, electronic device and readable storage medium for trajectory proximity inquiry," all contents of which are incorporated into the text by reference.

[0002] The present disclosure relates to the field of computer technology, and in particular to a method for trajectory proximity lookup, an apparatus, an electronic device, and a readable storage medium. Background Technology

[0003] A k-neighbor lookup refers to finding the k trajectories closest to a given trajectory in space based on fresh distance.

[0004] Traditional search techniques are mainly as follows: continuously expanding the range of the surrounding space around the search trajectory, while traversing all trajectories within this space and sorting them according to their distance from the search trajectory until the k closest trajectories are found.

[0005] However, with the widespread application of smart devices and location-based services, large-scale trajectory data is being generated, and traditional methods based on relational databases are no longer able to support large-scale data storage and analysis tasks.

[0006] Because the number of trajectory points on the trajectory is massive, the amount of calculation for fresh distance is large, and there are serious efficiency problems with existing trajectory proximity lookups.

[0007] It should be understood that the information disclosed in the background section above is used solely to enhance understanding of the background of this disclosure and may include information that does not constitute existing technology already known to a person skilled in the art. As background technology, the following prior art documents may be referenced. [1] YUAN J, ZHENG Y, XIE X, et al. Driving with knowledge from the physical world[C] / / Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining. 2011 : 316 - 324.[2] SHANG Z, LI G, BAO Z. Dita: Distributed in-memory trajectory analytics[C] / / Proceedings of the 2018 International Conference on Management of Data. 2018 : 725 - 740.

[0008] The purpose of the present disclosure is to provide a trajectory proximity lookup method, apparatus, electronic device, and readable storage medium to overcome, to some extent, the problem of low efficiency of trajectory proximity lookup in at least related technology.

[0009] Other features and advantages of the present disclosure will become apparent from subsequent detailed descriptions or will be partially acquired through the practice of the present disclosure.

[0010] According to one aspect of the present disclosure, a trajectory proximity lookup method is provided, comprising the steps of acquiring a first trajectory of a lookup target and determining spatial location information of the first trajectory; generating a trajectory signature according to the positional relationship between the spatial location information of the first trajectory and the lookup target area; determining a spatial location index code of the first trajectory through XZ-Ordering; and constructing a spatial range index of the first trajectory based on the trajectory signature and the spatial location index code.

[0011] In an embodiment of the present disclosure, the method further includes the step of determining a marker of the first trajectory and the step of adding the marker of the first trajectory to a postfix of the spatial range index.

[0012] In an embodiment of the present disclosure, the method further includes the steps of obtaining a random number of the first trajectory, adding the random number to a prefix of the spatial range index, and randomly storing the spatial range index in a distributed server according to the prefix.

[0013] In an embodiment of the present disclosure, the method further comprises the steps of: retrieving one search target area from a first priority queue in which the search target areas are stored; determining the code length of a spatial location index code of the search target area; and expanding the search target area or stopping the splitting of the search target area according to the size relationship between the code length and a preset length.

[0014] In an embodiment of the present disclosure, the step of expanding the search target area or stopping the division of the search target area according to the size relationship between the code length and the preset length includes: determining whether the code length is greater than the preset length; if it is determined that the code length is greater than the preset length, not dividing the search target area; and performing spatial range search processing within the search target area.

[0015] In an embodiment of the present disclosure, the step of expanding the search target area or stopping the splitting of the search target area according to the size relationship between the code length and the preset length further comprises: a step of determining whether the code length is greater than the preset length; and, if it is determined that the code length is less than or equal to the preset length, a step of generating a sub-node search target area of ​​the search target area by performing a four-branch tree recursive splitting of the search target area until the code length of the sub-node search target area becomes greater than or equal to the preset length.

[0016] In an embodiment of the present disclosure, after stopping the recursive splitting of the four-branch tree of the search target area, the method further includes the step of determining a second trajectory within the search target area and storing the second trajectory in a second priority queue.

[0017] In an embodiment of the present disclosure, the method further comprises the steps of determining a first fresh distance between the first trajectory and the search target area, determining whether the first fresh distance is greater than or equal to a maximum distance threshold, performing area pruning of the search target area if it is determined that the first fresh distance is greater than or equal to the maximum distance threshold, and updating the maximum distance threshold according to the result of the area pruning.

[0018] In an embodiment of the present disclosure, the method further comprises the steps of determining the lower boundary position of the first trajectory and the lower boundary position of the second trajectory within the inquiry target area, and performing a lower boundary pruning process for the second trajectory of the inquiry target area according to the lower boundary position of the first trajectory and the lower boundary position of the second trajectory, wherein the lower boundary position includes at least one of a starting point lower boundary position, an ending point lower boundary position, and a trajectory signature lower boundary position.

[0019] In an embodiment of the present disclosure, the step of performing a summer pruning process for the second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory includes the step of determining a starting point fresh distance between the starting point summer position of the first trajectory and the starting point summer position of the second trajectory, and the step of performing a first summer pruning process for the second trajectory according to the size relationship between the starting point fresh distance and a first preset distance.

[0020] In an embodiment of the present disclosure, the step of performing a summer pruning process for a second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further includes the step of determining an endpoint fresh distance between the endpoint summer position of the first trajectory and the endpoint summer position of the second trajectory, and the step of performing a second summer pruning process for the second trajectory according to the size relationship between the endpoint fresh distance and a second preset distance.

[0021] In an embodiment of the present disclosure, the step of generating a trajectory signature according to the positional relationship between the spatial position information of the first trajectory and the search target area further comprises: performing sequential encoding for four sub-node search target areas of the search target area; recording the sub-node search target area through which the first trajectory passes as a first marker and recording the sub-node search target area through which the first trajectory does not pass as a second marker; and determining the trajectory signature of the first trajectory according to the sequential encoding, the first marker, and the second marker.

[0022] In an embodiment of the present disclosure, the step of performing a summer pruning process for a second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further includes the step of determining a trajectory signature fresh distance between the trajectory signature summer of the first trajectory and the trajectory signature summer of the second trajectory, and the step of performing a third summer pruning process for the second trajectory according to the size relationship between the trajectory signature fresh distance and a third preset distance.

[0023] According to another aspect of the present disclosure, a trajectory proximity lookup device is provided, comprising: an acquisition module configured to acquire a first trajectory of a lookup target and determine spatial location information of the first trajectory; a signature module configured to generate a trajectory signature according to the positional relationship between the spatial location information of the first trajectory and the lookup target area; a determination module configured to determine a spatial location index code of the first trajectory through XZ-Ordering; and an index module configured to construct a spatial range index of the first trajectory based on the trajectory signature and the spatial location index code.

[0024] According to another aspect of the present disclosure, an electronic device is provided, comprising a processor and a memory for storing executable instructions of said processor, said processor is configured to execute said executable instructions to perform any trajectory proximity inquiry method described above.

[0025] According to another aspect of the present disclosure, a computer-readable storage medium is provided, and a computer program is stored that implements any of the above-described trajectory proximity lookup methods when executed by a processor.

[0026] The trajectory proximity lookup method provided in the embodiment of the present disclosure improved the indexing and lookup efficiency of the lookup target area by constructing a spatial range index of the first trajectory, and improved the efficiency and accuracy of determining a trajectory close to the lookup target trajectory within the lookup target area.

[0027] Furthermore, by pruning the target area of ​​the inquiry through area pruning, the inquiry range of the second trajectory was simplified, the efficiency of spatial range inquiry was increased, and the inquiry process was accelerated.

[0028] Going a step further, by performing summer pruning on the second trajectory, the computational load of fresh distance was reduced, and unnecessary trajectory queries and query times were minimized. Finally, by randomly storing spatial range indexes on distributed servers, the maintenance pressure of trajectory data was lowered, and the reliability of trajectory proximity queries was improved.

[0029] It should be understood that the general description above and the detailed description in the following text are illustrative and interpretive only and are not to limit the present disclosure. Brief explanation of the drawing

[0030] The drawings attached herein have been incorporated into the specification to form part of the specification and present embodiments conforming to the present disclosure, and have been used together with the specification to explain the principles of the present disclosure. To be clear, the drawings in the following description are merely some embodiments of the present disclosure, and other drawings can be obtained based on these drawings without requiring creative labor by a person skilled in the art. FIG. 1A shows a schematic diagram of the code for a trajectory proximity lookup scheme of the present disclosure embodiment. FIG. 1B shows a schematic diagram of the code for a trajectory proximity lookup scheme of the present disclosure embodiment. FIG. 1C shows a schematic diagram of the code for a trajectory proximity lookup scheme of the present disclosure embodiment. FIG. 1D shows a schematic diagram of the code for a trajectory proximity lookup scheme of the present disclosure embodiment. FIG. 2 shows a flowchart of a trajectory proximity inquiry method of an embodiment of the present disclosure. FIG. 3 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 4 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 5 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 6 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 7 shows a flowchart of another trajectory proximity lookup method of the present disclosure embodiment. FIG. 8 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 9 shows a flowchart of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 10 shows a flowchart of another trajectory proximity lookup method of the present disclosure embodiment. FIG. 11 shows a flowchart of another trajectory proximity lookup method of the present disclosure embodiment. FIG. 12 shows a flowchart of another trajectory proximity lookup method of the present disclosure embodiment. FIG. 13 shows a flowchart of another trajectory proximity lookup method of the present disclosure embodiment. FIG. 14 shows a schematic diagram of a trajectory proximity inquiry method of an embodiment of the present disclosure. FIG. 15 shows a schematic diagram of another trajectory proximity inquiry method of the present disclosure embodiment. FIG. 16 shows a schematic diagram of the test results of the trajectory proximity inquiry method of the present disclosure embodiment. FIG. 17 shows a schematic diagram of the test results of the trajectory proximity inquiry method of the present disclosure embodiment. FIG. 18 shows a schematic diagram of the test results of the trajectory proximity inquiry method of the present disclosure embodiment. FIG. 19 shows a schematic diagram of the test results of the trajectory proximity inquiry method of the present disclosure embodiment. FIG. 20 shows a schematic diagram of a trajectory proximity inquiry device of an embodiment of the present disclosure. FIG. 21 shows a schematic diagram of an electronic device of an embodiment of the present disclosure. Specific details for implementing the invention

[0031] Now, with reference to the drawings, exemplary implementations will be described more comprehensively. However, exemplary implementations may be implemented in various forms and should not be understood as being limited to the legends described herein. Instead, by providing such implementations, the present disclosure becomes more comprehensive and complete, and the concept of exemplary implementations can be fully conveyed to those skilled in the art. The described features, structures, or characteristics may be combined in a manner suitable for one or more implementations.

[0032] Additionally, the attached drawings are merely schematic representations of the present disclosure and are not necessarily drawn in proportion. Identical reference numerals in the drawings indicate identical or similar parts, so redundant descriptions are omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. Such functional entities may be implemented in software form, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0033] The method provided in the present disclosure constructs a spatial range index of a first trajectory to improve the indexing and querying efficiency of the target area, and further improves the efficiency and accuracy of determining trajectories close to the target trajectory within the target area. Furthermore, by pruning the target area through area pruning, the query range of the second trajectory is simplified, the efficiency of spatial range querying is improved, and the query process is accelerated. Going a step further, by performing summer pruning on the second trajectory, the computational amount of fresh distance is reduced, and unnecessary trajectory queries and query times are reduced. Finally, by randomly storing the spatial range index on a distributed server, the maintenance pressure on trajectory data is reduced, and the reliability of trajectory proximity queries is improved.

[0034] As illustrated in FIG. 1, the trajectory proximity inquiry method of the present disclosure includes the following key concepts.

[0035] (1) GPS Point (GPSPoint): A GPS point p=(lat; lng;t) includes latitude lat, longitude lng and time stamp t, indicating that the object of movement is at the geographical coordinate location (lat; lng) at time t.

[0036] (2) Trajectory: A single trajectory It is a sequence constructed by arranging GPS points generated from the same moving target in chronological order. That is, .

[0037] (3) Path: Path is a set of continuous intervals, and the order of the intervals is the order in which objects move. Generally, a single natural number is used to represent the interval marker.

[0038] (4) MapMatchTrajectory: The trajectory is mapped into segments through a map matching algorithm to obtain the mapMatchTrajectory. It can form. Here, e i indicates a sign for a road network section, and t i indicates the time when the target of movement enters the corresponding section. Unless otherwise specified in the description below, the trajectory is the trajectory after matching.

[0039] (5) PathTemporalRangeQuery: Path P, time range If a matching trajectory set T is specified, a trajectory proximity lookup is all matching trajectories tr within T i While searching for, which of the sub-trajectories ... passes through path P within the given period. That is, .

[0040] (6) NoSQL: Generally refers to a non-relational database, and its data storage does not require a fixed table mode. It was created to solve the challenges caused by the multiple data types in big data sets, particularly the difficulties in big data applications.

[0041] (7) HBase: A highly reliable, high-performance, column-oriented, and flexible distributed storage system that can build large-scale structured storage clusters on low-cost facilities and is a type of NoSQL.

[0042] (8) Fresh Street: , is a path space similarity description commonly used to measure similarity between trajectories.

[0043] (9) XZ-Ordering: A spatial encoding method of the filling curve that combines time information.

[0044] (10) Priority queue: A common data structure in which elements are assigned priorities and the element with the highest priority is deleted first. Therefore, compared to the first-in, first-out of a standard queue, a priority queue has the characteristic of selecting the highest priority.

[0045] The solution provided in the present disclosure embodiments relates to technologies such as postfix trees, path decomposition, and distributed architectures, and is specifically described through the following embodiments.

[0046] The aforementioned trajectory proximity lookup method can be realized through the interaction of multiple terminals and server clusters.

[0047] The terminal may be a mobile terminal such as a mobile phone, game console, tablet, e-book reader, smart glasses, MP4 (Moving Picture Experts Group Audio Layer IV) player, smart home device, AR (Augmented Reality) device, VR (Virtual Reality) device, etc., or the terminal may be a personal computer (PC) such as a laptop and desktop computer.

[0048] An application for providing trajectory proximity lookup can be installed on the terminal.

[0049] The terminal and the server cluster are connected via a communication network. Optionally, the communication network is a wired or wireless network.

[0050] A server cluster is a single server, a server or virtualization platform composed of multiple servers, or a cloud computing service center. Server clusters are used to provide background services to applications that provide trajectory proximity lookups. Optionally, the server cluster handles primary computing tasks and the terminal handles secondary computing tasks, or the server cluster handles secondary computing tasks and the terminal handles primary computing tasks, or co-computing is performed using a distributed computing architecture between the terminal and the server cluster.

[0051] In some selectable embodiments, a postfix tree index is used to index the original string and can improve the performance of string postfix search. In track data management, the track after matching can be viewed as a string, and each segment marker is equivalent to a single character of the string, and path lookup (without considering time filtering conditions) can be mapped to the problem of searching for string postfixes. That is, searching using a sequence of segment markers can be viewed as searching using a sequence of characters.

[0052] Optionally, the client of an application installed on different terminals is the same, or the client of an application installed on two terminals is a client of the same type of application on different control system platforms. Depending on the terminal platform, the specific form of this application client may also differ. For example, this application client may be a mobile phone client, a PC client, or a global wide area network client.

[0053] Those skilled in the art will understand that the number of the aforementioned terminals may be greater or less. For example, the aforementioned terminal may be only one, or the number of the aforementioned terminals may be tens, hundreds, or more. The embodiments of the present disclosure do not limit the number of terminals or the type of device.

[0054] Optionally, this system may also include a management device connected to the server cluster via a communication network. Optionally, the communication network is a wired or wireless network.

[0055] Optionally, the wireless or wired network uses standard communication technologies and / or protocols. The network is generally the Internet but may be any network and includes, but is not limited to, any combination of Local Area Networks (LAN), Metropolitan Area Networks (MAN), Wide Area Networks (WAN), mobile, wired or wireless networks, private networks, or virtual private networks. In some embodiments, data exchanged over the network is represented using technologies and / or formats including Hyper Text Markup Language (HTML), Extensible Markup Language (XML), etc. Additionally, all or some links may be encrypted using common encryption technologies such as Secure Socket Layer (SSL), Transport Layer Security (TLS), Virtual Private Network (VPN), and Internet Protocol Security (IPsec). In other embodiments, these data communication technologies may be replaced or supplemented with custom and / or private data communication technologies.

[0056] The following describes each step of the trajectory proximity lookup method of this exemplary implementation method in more detail by combining drawings and examples.

[0057] FIG. 2 shows a flowchart of a trajectory proximity lookup method according to an embodiment of the present disclosure. The method provided in the present disclosure can be performed on any electronic device equipped with computing processing capabilities, and a server cluster is described as an exemplary execution entity.

[0058] As illustrated in FIG. 2, the server cluster performs a trajectory proximity lookup method including the following steps.

[0059] In step S202, a first trajectory of the inquiry target is obtained, and spatial location information of the first trajectory is determined.

[0060] In step S204, a trajectory signature is generated based on the spatial position information of the first trajectory and the positional relationship between the search target area.

[0061] In the above embodiment, the area to be searched It is divided into regions of equal size, where β is an integer greater than or equal to 1, and each region is encoded starting from 0. That is, the spatial position information of trajectory tr is It is represented as a binary sequence.

[0062] For example, if at least one GPS point in the trajectory is located in a certain area, the corresponding binary position is 1, and otherwise it is 0.

[0063] In step S206, the spatial position index code of the first trajectory is determined using XZ-Ordering.

[0064] In the above embodiment, the spatial position index code is a code generated based on XZ-Ordering, first obtaining a quaternary sequence of the trajectory and then converting this quaternary sequence into a long decimal integer.

[0065] In step S208, a spatial range index of the first trajectory is constructed based on the trajectory signature and the spatial position index code.

[0066] In the above-described embodiment, a spatial range index of the first trajectory was constructed to improve the index and query efficiency of the query target area, and furthermore, the efficiency and accuracy of determining a trajectory close to the query target trajectory within the query target area were improved. Furthermore, by pruning the query target area through area pruning, the query range of the second trajectory was simplified, the efficiency of spatial range querying was increased, and the query process was accelerated. Going a step further, by pruning the second trajectory, the amount of computation for fresh distance was reduced, and unnecessary trajectory queries and query times were reduced.

[0067] Based on the steps of FIG. 2, as illustrated in FIG. 3, the trajectory proximity lookup method further includes the following steps.

[0068] In step S302, the marker of the first trajectory is determined.

[0069] In step S304, the marker of the first trajectory is added to the postfix of the spatial range index.

[0070] In the above embodiment, the marker of the first trajectory is added to the postfix of the spatial range index to support spatial range lookup. That is, if a lookup space is provided, all trajectory records within that space can be looked up.

[0071] Based on the steps of FIG. 2, as illustrated in FIG. 4, the trajectory proximity lookup method further includes the following steps.

[0072] In step S402, the random number of the first trajectory is obtained.

[0073] In step S404, the random number is added to the prefix of the space range index.

[0074] In step S406, the spatial range index is randomly stored in a distributed server according to the prefix.

[0075] In the above-described embodiment, by randomly storing the spatial range index on distributed servers, data can be effectively distributed to different data servers, thereby improving load balancing and the pressure of data hotspots, reducing the pressure of maintaining high-level trajectory data, and improving the reliability of trajectory proximity lookups.

[0076] Based on the steps of FIG. 2, as illustrated in FIG. 5, the trajectory proximity lookup method further includes the following steps.

[0077] In step S502, one search target area is retrieved from the first priority queue where the search target areas are stored.

[0078] In step S504, the code length of the spatial location index code of the search target area is determined.

[0079] In step S506, depending on the size relationship between the code length and the preset length, the search target area is expanded or the splitting of the search target area is stopped.

[0080] In the above-described embodiment, since a larger code length of the spatial position index code of the search target area indicates that the spatial representation of the trajectory is more accurate, the precision of the search target area is controlled using a preset length.

[0081] Based on the steps shown in FIG. 2 and FIG. 5, as illustrated in FIG. 6, the step of expanding the search target area or stopping the division of the search target area according to the size relationship between the code length and the preset length includes the following steps.

[0082] In step S6062, it is determined whether the code length is greater than the preset length; if it is greater, step S6064 is performed, otherwise, step S6068 is performed.

[0083] In step S6064, if it is determined that the code length is greater than the preset length, the search target area is not split.

[0084] In step S6066, spatial range lookup processing is performed within the above-mentioned target area.

[0085] In the above-described embodiment, if it is determined that the code length is greater than the preset length, spatial range inquiry processing is performed within the search target area without dividing the search target area, thereby effectively reducing the search range of the second trajectory under the premise of securing search precision.

[0086] Based on the steps shown in FIG. 2 and FIG. 5, as illustrated in FIG. 6, the step of expanding the search target area or stopping the division of the search target area according to the size relationship between the code length and the preset length further includes the following steps.

[0087] In step S6062, it is determined whether the code length is greater than the preset length.

[0088] In step S6068, if it is determined that the code length is less than or equal to the preset length, recursive splitting of the four-branched tree of the search target area is performed until the code length of the sub-node search target area becomes greater than or equal to the preset length, thereby creating the sub-node search target area of ​​the search target area.

[0089] In the above embodiment, if it is determined that the code length is less than or equal to the preset length, the splitting process of the search target area is accurately controlled by performing recursive four-branch tree splitting of the search target area until the code length of the sub-node search target area becomes greater than or equal to the preset length.

[0090] Based on the steps of FIG. 2, as illustrated in FIG. 7, the trajectory proximity lookup method further includes the following steps.

[0091] In step S702, after stopping the recursive splitting of the four-branched tree of the search target area, a second trajectory within the search target area is determined and the second trajectory is stored in a second priority queue.

[0092] In the above embodiment, after stopping the recursive splitting of the four-branched tree of the search target area, a second trajectory within the search target area is determined and the second trajectory is stored in a second priority queue, and the number of second trajectories in the second priority queue satisfies the requirements for the number of searches.

[0093] In addition, the second trajectory in the second priority queue also has a priority, and the element with the highest priority is deleted first. That is, in the subsequent summer pruning process, the second trajectory that satisfies the lookup distance requirement can be obtained more quickly by being pruned preferentially.

[0094] Specifically, if the code sequence length of the target region is less than a constant g specified by the system, the sub-nodes of the four-branched trees of the target region are added to the first priority queue, and then the next region within the first priority queue is checked. When the code sequence length of the target region reaches the given constant g, the target region is no longer split, and a spatial range lookup is performed using the target region directly to obtain the trajectory result set T. SR Acquires.

[0095] Based on the steps of FIG. 2, as illustrated in FIG. 8, the trajectory proximity lookup method further includes the following steps.

[0096] In step S802, a first fresh distance between the first trajectory and the inquiry target area is determined.

[0097] In step S804, it is determined whether the first fresh distance is greater than or equal to the maximum distance threshold, and if so, step S806 is performed, and if not, step S810 is performed.

[0098] In step S806, if it is determined that the first fresh distance is greater than or equal to the maximum distance threshold, area pruning processing of the inquiry target area is performed.

[0099] In step S808, the maximum distance threshold is updated according to the result of the area pruning process.

[0100] In step S810, the second trajectory within the inquiry target area is queried.

[0101] In the above-described embodiment, the inventor, through verification and reasoning, if If it is It was confirmed that there exist cases where this is established, is the fresh distance between the trajectory and the search target space. Here, the trajectory tr is the first trajectory retrieved when querying a spatial range in the search target space.

[0102] Specifically, if the second trajectory was not the first one retrieved, that is, if it was retrieved from a previous "internal" search area, it would have been checked whether there was a result set of k adjacent trajectory searches.

[0103] In addition, if the second trajectory is the first one retrieved, the following relationship holds.

[0104] Based on this, by pruning the search target area through the first fresh distance, the invalid area of ​​the search target area can be effectively removed, and furthermore, the efficiency and reliability of the trajectory proximity search can be improved.

[0105] Based on the steps of FIG. 2, as illustrated in FIG. 9, the trajectory proximity lookup method further includes the following steps.

[0106] In step S902, the lower boundary position of the first trajectory and the lower boundary position of the second trajectory within the inquiry target area are determined.

[0107] In step S904, a sub-pruning process is performed on the second trajectory of the inquiry target area according to the sub-location of the first trajectory and the sub-location of the second trajectory. The sub-location includes at least one of a start point sub-location, an end point sub-location, and a trajectory signature sub-location.

[0108] In the above-described embodiment, by performing pruning processing using the fresh distance between the summer position of the first trajectory and the summer position of the second trajectory, the amount of computation for calculating distances for all trajectory points of the first trajectory and the second trajectory was prevented and the time complexity was reduced.

[0109] Based on the steps of FIG. 2 and as illustrated in FIG. 10, the step of performing summer pruning for the second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory includes the following steps.

[0110] In step S1002, the starting point fresh distance between the starting point summer position of the first trajectory and the starting point summer position of the second trajectory is determined.

[0111] In step S1004, a first summer pruning process is performed on the second trajectory according to the size relationship between the starting point fresh distance and the first preset distance.

[0112] Based on the steps of FIG. 2 and FIG. 9, as illustrated in FIG. 11, the step of performing a summer pruning process for the second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further includes the following steps.

[0113] In step S11042, the endpoint fresh distance between the endpoint lower position of the first trajectory and the endpoint lower position of the second trajectory is determined.

[0114] In step S11044, a second summer pruning process is performed on the second trajectory according to the size relationship between the endpoint fresh distance and the second preset distance.

[0115] In the above embodiment, based on the start and end points of the trajectory, the present disclosure proposes a lower bound (lower_bound() return value is an iterator and returns a position pointing to the first value that is equal to or greater than the key) of the start / end point distance of similar trajectories. If the lower bound distance is greater than a specified similarity threshold ε, the first trajectory and the second trajectory are not necessarily similar, and based on this, rapid pruning is performed on the second trajectory of the search target area.

[0116] Based on the step of FIG. 2, as illustrated in FIG. 12, the step of generating a trajectory signature according to the positional relationship between the spatial position information of the first trajectory and the inquiry target area further includes the following steps.

[0117] In step S12042, sequential encoding is performed on the four sub-nodes of the above-mentioned search target area.

[0118] In step S12044, the sub-node inquiry target area through which the first trajectory passes is recorded as the first marker, and the sub-node inquiry target area through which the first trajectory does not pass is recorded as the second marker.

[0119] In step S12046, the trajectory signature of the first trajectory is determined according to the sequential encoding, the first marker, and the second marker.

[0120] In the above embodiment, the first label can be a binary "1" and the second label can be a binary "0", and a unique trajectory signature is generated according to the order of sequential encoding.

[0121] Based on the steps of FIG. 2 and FIG. 9, as illustrated in FIG. 13, the step of performing a summer pruning process for the second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further includes the following steps.

[0122] In step S13042, the trajectory signature fresh distance between the trajectory signature summer of the first trajectory and the trajectory signature summer of the second trajectory is determined.

[0123] In step S13044, a third summer pruning process is performed on the second trajectory according to the size relationship between the trajectory signature fresh distance and the third preset distance.

[0124] In the above embodiment, the inventor, through verification and reasoning, if If so, It was confirmed that this is established.

[0125] Proof: Which point and In this case, they must be either the query target area q or the trajectory tr, or the signature area and It will be located at.

[0126] Therefore, the following can be proven:

[0127] Here, the computational time complexity of SIG_LB is , and, Since it is considered a constant, it can still significantly improve the filtering effect.

[0128] Based on this, since the trajectory signature can represent the position information of the trajectory more accurately, the present disclosure provides means for a signature sub-value. If the signature sub-value of two trajectories is greater than a given threshold ε, the first trajectory and the second trajectory will not necessarily be similar, and more efficient and faster pruning will be performed for the second trajectory of the search target area.

[0129] FIGS. 14 to 19 show embodiments of a trajectory proximity lookup method. In a trajectory k proximity lookup, the present disclosure considers a spatial range lookup as a sub-operation.

[0130] As illustrated in FIG. 14, when specifying a search trajectory q and a distance threshold ε (assuming in this disclosure that the units have already been converted from length to spatial coordinate degrees), two spatial regions, i.e. and You can obtain. Here, GPS points class are the start and end points of the lookup trajectory q, respectively. Fresh distance f F In this case, all trajectories similar to q must be the result of a spatial range lookup It is included in.

[0131] MBR (Minimum Bounding Rectangle) Pruning: Specify the lookup trajectory q and similarity threshold ε, and . The present disclosure is within a single spatial range It is possible to obtain , and all MBRs of trajectories similar to q are necessarily completely contained in S.

[0132] Referring to FIG. 15, the inventor [describes] a first trajectory tr 1 and the second trajectory tr 2 Regarding the similarity of [the term], summer pruning and trajectory signature pruning were proposed, and the following theorem was proposed to verify the improvement in the reliability and efficiency of trajectory proximity lookup.

[0133] Theorem 1. Similar Trajectory Lookup Completeness Theorem: Fresh distance f F In this case, all trajectories similar to the given search trajectory are in set T'.

[0134] Theorem 2. Area Pruning Theorem: If If so, , where trajectory tr is the trajectory first retrieved through spatial range lookup by r.

[0135] Theorem 3. MBR Pruning Theorem: If a trajectory tr is not completely contained within region S, that is, if at least one GPS point p of tr is located outside region S, then for fresh distance, tr will not necessarily be similar to q.

[0136] Theorem 4. Start / End Point Lower Branch Pruning Theorem: If ,then . if , then .

[0137] Summary 5. Signature Summer Pruning Summary: If ,then .

[0138] According to an embodiment of the present disclosure, a lookup point q, a fresh distance function f F , if you input the number of trajectories k to return, the output is the k-nearest point lookup trajectory result set T. knn And, specifically, it can be divided into the following three steps.

[0139] Query Phase 1: Primarily initializes various variables. Here, cdq is a second priority queue used to store the second trajectory, req identifies the first priority queue and records the range of spatial regions to be examined, and d max is the maximum value of all trajectory distances within the current lookup trajectory q and cdq.

[0140] Query Step 2: Draw one spatial region r from req. The candidate set cdq already contains k trajectories, and the distance between spatial region r and query trajectory q is dmax If it is greater than, this means that unsearched trajectories are not included in the result set (see Theorem 2, referred to as area pruning in this disclosure), and the search process can be terminated.

[0141] If the length of the code sequence of r is less than a constant g specified by the system, the present disclosure adds the child nodes of the four-branched tree of r to req and then checks the next region of req.

[0142] When the code sequence length of r reaches a given constant g, the present disclosure performs a spatial range lookup using r directly without further splitting r to obtain a result set T SR Acquires.

[0143] Each trajectory In the case of , since the time overhead of similarity between trajectories is too large, the present disclosure proposes two summer pruning strategies.

[0144] If tr satisfies all the subordinate conditions described above, the present disclosure adds it to the candidate result set cdq and then d max Updates.

[0145] Query Step 3: When all candidate regions of req have completed the inspection, the present disclosure returns the trajectory within candidate result cdq as the final result.

[0146] FIGS. 16 to 19 provide performance test results and inquiry performance results of the trajectory proximity inquiry of the present disclosure.

[0147] (1) Performance test results

[0148] The present disclosure verifies the performance of the method presented in the present disclosure using two datasets: 1) T-Drive[1], which is a public dataset containing GPS point information of over 10,000 taxis in Beijing, with a time range of 7 days from February 2, 2008 to February 8, 2008; 2) Lorry, which is a truck GPS trajectory dataset containing one month's GPS trajectory information of nearly 50,000 JD Logistics trucks in Guangzhou, with a time range of 1 March 1, 2014 to 31 March 2014. In the present disclosure, trajectories are processed using Spark preprocessing and HBase is used as the underlying NoSQL storage. All experiments are performed on a cluster with 5 nodes, each node equipped with a CentOS 7.4 operating system, an 8-core CPU, 32GB of memory, and 1TB of plain mechanical disk.

[0149] As can be seen in FIGS. 16 and 17, the method presented in this disclosure is a TM, and presents three comparative experiments: 1) Dita, which is a representative memory-based trajectory management system, which presents an effective data partitioning method, solves data locality problems, and also presents cost-based technology to achieve load balancing, and the main concept is to identify representative GPS points and then design a tree-structured index based on these representative points to efficiently filter dissimilar trajectories; 2) , this is a variant of the TM method that does not use PosCode technology in spatial range index tables; 3) This is another variant of the TM method that does not use a summer pruning strategy during the similar lookup process.

[0150] Considering the similar measurements of the trajectory, the present disclosure relates to a fresh distance f F Adopting, and other distance measurement functions, for example, the Hausdorff distance fH and dynamic time warping f D The experimental results are similar.

[0151] (2) Comparison of query performance.

[0152] As shown in Figures 18 and 19, the changes in similar lookup times for different amounts of data were compared. The similarity threshold was accepted as 3 km.

[0153] To speak of all methods, similarity lookups take more time as the amount of data increases. This is because the larger the amount of data, the more trajectories are returned under the same similarity threshold. TM is It is slightly faster, because the underlying call of a similar lookup is a spatial range lookup. Here, PosCode can reduce unnecessary trajectory scans and improve lookup efficiency.

[0154] If the summer pruning filtering algorithm is not used, the present disclosure must call the fresh distance calculation formula to verify all trajectories satisfying the spatial range lookup, which is very time-consuming, so It is slower than TM. Dita is much slower than TM. As mentioned earlier, Dita builds large indexes in memory and spends a lot of time scanning index files for each lookup.

[0155] TM can directly create a lookup window and then switch to a parallel SCAN operation at the lower level. Because it requires a lot of memory overhead, Dita has high demands on clusters and limited scalability.

[0156] In fact, if the Lorry load dataset exceeds 60%, Dita throws a memory overflow exception but TM can still function well, and even if the Lorry dataset reaches 100%, TM can operate reliably. This demonstrates the strong scalability of the TM method.

[0157] As shown in FIGS. 18 and 19, similarity threshold With the increase of, the time overhead of similar queries also increases slightly in all methods. This is because it returns more trajectories that satisfy the conditions. TM and its variants are much faster than Dita and sometimes even reach three numerical levels of efficiency improvement. This further demonstrates the efficiency of the present disclosure.

[0158] Next, a trajectory proximity lookup device (2000) according to this implementation of the present disclosure will be described with reference to FIG. 20. The trajectory proximity lookup device (2000) illustrated in FIG. 20 is merely one example and should not be used to limit the function and scope of use of the embodiments of the present disclosure.

[0159] The trajectory proximity lookup device (2000) is represented as a hardware module. The components of the trajectory proximity lookup device (2000) may include, but are not limited to, an acquisition module (2002), a signature module (2004), a determination module (2006), and an index module (2008).

[0160] The acquisition module (2002) is configured to acquire a first trajectory of the inquiry target and determine spatial location information of the first trajectory.

[0161] The signature module (2004) is configured to generate a trajectory signature based on the spatial location information of the first trajectory and the positional relationship between the inquiry target area.

[0162] The determination module (2006) is configured to determine the spatial position index code of the first trajectory using XZ-Ordering.

[0163] The index module (2008) is configured to construct a spatial range index of the first trajectory based on the trajectory signature and the spatial position index code.

[0164] The present disclosure presents a method for trajectory proximity lookup and improves the efficiency of indexing and lookup of the target area by constructing a spatial range index of the first trajectory, and further improves the efficiency and accuracy of determining trajectories close to the target trajectory within the target area. Furthermore, by pruning the target area through area pruning, the lookup range of the second trajectory is simplified, the efficiency of spatial range lookup is increased, and the lookup process is accelerated. Going a step further, by performing downward pruning on the second trajectory, the computational amount of fresh distance is reduced, and unnecessary trajectory lookups and lookup times are reduced. Finally, by randomly storing the spatial range index on a distributed server, the maintenance pressure on trajectory data is reduced and the reliability of trajectory proximity lookup is improved.

[0165] Referring to FIG. 21 below, an electronic device (2100) according to this implementation of the present disclosure will be described. The electronic device (2100) shown in FIG. 21 is merely one example and should not be given any limitations on the function and scope of use of the embodiments of the present disclosure.

[0166] As illustrated in FIG. 21, the electronic device (2100) is represented as a general-purpose computing device. Components of the electronic device (2100) may include, but are not limited to, at least one processing unit (2110) described above, at least one storage unit (2120) described above, and a bus (2130) connecting different system components including the storage unit (2120) and the processing unit (2110).

[0167] The storage unit stores program code, and the program code can be executed by the processing unit (2110), and the processing unit (2110) can execute the procedures of various exemplary implementations of the present disclosure described in the above-described "exemplary methods" section of the present specification. For example, the processing unit (2110) can perform steps of the trajectory proximity lookup method illustrated in FIGS. 2 through 13 and other steps limited to the trajectory proximity lookup method of other embodiments of the present disclosure.

[0168] The storage unit (2120) may include a readable medium in the form of a volatile storage unit such as a random access storage unit (RAM) (21201) and / or a cache storage unit (21202), and may additionally include a read-only storage unit (ROM) (21203).

[0169] The storage unit (2120) may further include a program / utility (21204) having one or more program modules (21205), and such program modules (21205) include, but are not limited to, an operating system, one or more applications, other program modules and program data, and each combination of such examples may include an implementation of a network environment.

[0170] The bus (2130) may represent one or more of several bus structures and includes a storage unit bus or a storage unit controller, a peripheral bus, a graphics acceleration port, a processing unit, or a LAN bus using any of the several bus structures.

[0171] The electronic device (2100) may communicate with one or more external devices (2140), such as a keyboard, a pointing device, a Bluetooth device, etc., and may communicate with one or more devices that allow a user to interact with the electronic device, and / or may communicate with any device (e.g., a router, a modem, etc.) that allows the electronic device (2100) to communicate with one or more other computing devices. This communication may be performed through an input / output (I / O) interface (2150). Additionally, the electronic device (2100) may communicate with one or more networks (e.g., a LAN, a WAN, and / or a public network, e.g., the Internet) through a network adapter (2160). The network adapter (2160) communicates with other modules of the electronic device (2100) through a bus (2130). It should be noted that although not shown in the drawings, other hardware and / or software modules including, but not limited to, microcode, device drives, redundancy processing units, external disk drive arrays, RA identification systems, tape drives, data backup storage systems, etc. may be used in combination with electronic devices.

[0172] Through the description of the implementation method described above, those skilled in the art will easily understand that the exemplary implementation method described herein may be realized through software or by combining software with necessary hardware. Accordingly, the technical proposal according to the implementation method disclosed herein may be implemented in the form of a software product, which may be stored on a non-volatile storage medium (CD-ROM, USB, removable hard disk, etc.) or a network, and may include various instructions to enable a single computing device (personal computer, server, terminal device, or network device, etc.) to perform the method according to the implementation method disclosed herein.

[0173] In exemplary embodiments of the present disclosure, a computer-readable storage medium is also provided that stores a program product capable of implementing the methods described above in the present specification. In some possible implementations, each aspect of the present disclosure may be realized in the form of a program product, which includes program code, and when the program product is executed on a terminal device, the program code causes the terminal to perform a procedure according to the various exemplary implementations of the present disclosure described in the "exemplary methods" section described above in the present specification.

[0174] According to a program product for realizing the method described above in an implementation of the present disclosure, the program code may be included using a CD-ROM (portable compact disc read-only memory) and may be executed on a terminal device such as a personal computer. However, the program product of the present disclosure is not limited thereto. A readable storage medium in this specification may be any type of medium that includes or stores a program. This program may be used by or in combination with a system, device, or component.

[0175] A computer-readable signal medium may include a data signal that is contained in the baseband or propagated as part of a carrier wave, and which carries readable program code. Such propagated data signals may adopt various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A readable signal medium may also be any readable medium other than a readable storage medium that transmits, propagates, or transmits a program used or in conjunction with a command execution system, device, or device.

[0176] Program code contained in a readable medium can be transmitted to any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc.

[0177] Program code used to perform the tasks of the present disclosure may be written by combining one or more programming languages. These programming languages ​​include object-oriented programming languages ​​such as Java and C++, and general programming languages ​​such as the "C" language or similar programming languages. The program code may be executed entirely on a user computing device, partially on a user device, as a separate package, partially on a user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device or to an external computing device through any type of network, including a Local Area Network (LAN) or a World Area Network (WAN) (e.g., connected via the Internet using an Internet service operator).

[0178] Although several modules or units of the device used for executing operations have been mentioned in the detailed description above, it should be noted that this distinction is not mandatory. In practice, depending on the implementation method of the present disclosure, the features and functions of two or more modules or units described above may be embodied in a single module or unit. Conversely, the features and functions of a single module or unit described above may be divided and embodied across multiple modules or units.

[0179] Additionally, although each step of the method of the present disclosure is described in a specific order in the accompanying drawings, there is no requirement or implied that these steps must be performed in a specific order or that all indicated steps must be performed to achieve the desired result. Additional or alternative methods may be used, such as omitting some steps, combining several steps into one step, and / or dividing one step into several steps.

[0180] Through the description of the implementation method described above, those skilled in the art will easily understand that the exemplary implementation method described herein may be realized through software or by combining software with necessary hardware. Accordingly, the technical proposal according to the implementation method disclosed herein may be implemented in the form of a software product, which may be stored on a non-volatile storage medium (CD-ROM, USB, removable hard disk, etc.) or a network, and may include various instructions to enable a single computing device (personal computer, server, terminal device, or network device, etc.) to perform the method according to the implementation method disclosed herein.

[0181] Those skilled in the art will readily conceive of other embodiments of the present disclosure after practicing the specification and the invention disclosed herein. The present disclosure is intended to encompass all variations, uses, or adaptations of the present disclosure, such variations, uses, or adaptations, in compliance with the generality principle of the present disclosure, and include common knowledge or conventional technical means in the art that are not disclosed in the present disclosure. The specification and embodiments are to be regarded merely as illustrative, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

Claim 1 A trajectory proximity lookup method executed by a processing unit, comprising: a step of acquiring a first trajectory of a lookup target and determining spatial location information of the first trajectory; a step of generating a trajectory signature according to the positional relationship between the spatial location information of the first trajectory and the lookup target area; a step of determining a spatial location index code of the first trajectory through XZ-Ordering; a step of constructing a spatial range index of the first trajectory based on the trajectory signature and the spatial location index code; a step of determining a lower boundary position of the first trajectory and a lower boundary position of a second trajectory within the lookup target area; and a step of performing a lower boundary pruning process for the second trajectory of the lookup target area according to the lower boundary position of the first trajectory and the lower boundary position of the second trajectory, wherein the lower boundary position includes at least one of a starting point lower boundary position, an ending point lower boundary position, and a trajectory signature lower boundary position. Claim 2 A method for checking trajectory proximity according to claim 1, further comprising the steps of determining a marker of the first trajectory and adding the marker of the first trajectory to a postfix of the spatial range index. Claim 3 A trajectory proximity lookup method according to claim 2, further comprising the steps of obtaining a random number of the first trajectory, adding the random number to a prefix of the spatial range index, and randomly storing the spatial range index in a distributed server according to the prefix. Claim 4 A trajectory proximity lookup method according to claim 1, further comprising the steps of: retrieving one search target area from a first priority queue in which the search target area is stored; determining the code length of a spatial location index code of the search target area; and expanding the search target area or stopping the splitting of the search target area according to the size relationship between the code length and a preset length. Claim 5 A trajectory proximity search method according to claim 4, wherein the step of expanding the search target area or stopping the division of the search target area according to the size relationship between the code length and the preset length comprises: a step of determining whether the code length is greater than the preset length; a step of not dividing the search target area if it is determined that the code length is greater than the preset length; and a step of performing spatial range search processing within the search target area. Claim 6 A trajectory proximity search method according to claim 4, wherein the step of expanding the search target area or stopping the division of the search target area according to the size relationship between the code length and the preset length further comprises: a step of determining whether the code length is greater than the preset length; and, if it is determined that the code length is less than or equal to the preset length, a step of performing recursive four-branch tree division of the search target area until the code length of the sub-node search target area becomes greater than or equal to the preset length to generate a sub-node search target area of ​​the search target area. Claim 7 A trajectory proximity lookup method according to claim 1, further comprising the step of stopping the recursive splitting of a four-branch tree of the search target area, determining a second trajectory within the search target area, and storing the second trajectory in a second priority queue. Claim 8 A trajectory proximity lookup method according to claim 1, further comprising: a step of determining a first fresh distance between the first trajectory and the search target area; a step of determining whether the first fresh distance is greater than or equal to a maximum distance threshold; a step of performing area pruning processing of the search target area if it is determined that the first fresh distance is greater than or equal to the maximum distance threshold; and a step of updating the maximum distance threshold according to the result of the area pruning processing. Claim 9 delete Claim 10 A method for trajectory proximity inquiry according to claim 1, wherein the step of performing a summer pruning process for the second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory comprises: a step of determining a starting point fresh distance between the starting point summer position of the first trajectory and the starting point summer position of the second trajectory; and a step of performing a first summer pruning process for the second trajectory according to the size relationship between the starting point fresh distance and a first preset distance. Claim 11 A method for trajectory proximity inquiry according to claim 1, wherein the step of performing a summer pruning process for a second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further comprises the step of determining an endpoint fresh distance between the endpoint summer position of the first trajectory and the endpoint summer position of the second trajectory, and the step of performing a second summer pruning process for the second trajectory according to the size relationship between the endpoint fresh distance and a second preset distance. Claim 12 A method for trajectory proximity lookup according to claim 1, wherein the step of generating a trajectory signature according to the positional relationship between spatial position information of the first trajectory and a lookup target area further comprises: a step of performing sequential encoding for four sub-node lookup target areas of a lookup target area; a step of recording a sub-node lookup target area through which the first trajectory passes as a first marker and recording a sub-node lookup target area through which the first trajectory does not pass as a second marker; and a step of determining a trajectory signature of the first trajectory according to the sequential encoding, the first marker, and the second marker. Claim 13 A trajectory proximity inquiry method according to claim 1, wherein the step of performing a summer pruning process for a second trajectory of the inquiry target area according to the summer position of the first trajectory and the summer position of the second trajectory further comprises the step of determining a trajectory signature fresh distance between the trajectory signature summer of the first trajectory and the trajectory signature summer of the second trajectory, and the step of performing a third summer pruning process for the second trajectory according to the size relationship between the trajectory signature fresh distance and a third preset distance. Claim 14 A trajectory proximity inquiry device comprising: an acquisition module configured to acquire a first trajectory of a query target and determine spatial location information of the first trajectory; a signature module configured to generate a trajectory signature according to the positional relationship between the spatial location information of the first trajectory and the query target area; a determination module configured to determine a spatial location index code of the first trajectory through XZ-Ordering; an index module configured to construct a spatial range index of the first trajectory based on the trajectory signature and the spatial location index code; and a processing unit, wherein the processing unit determines a lower boundary position of the first trajectory and a lower boundary position of a second trajectory within the query target area, and performs a lower boundary pruning process for the second trajectory of the query target area according to the lower boundary position of the first trajectory and the lower boundary position of the second trajectory, wherein the lower boundary position includes at least one of a starting point lower boundary position, an ending point lower boundary position, and a trajectory signature lower boundary position. Claim 15 An electronic device characterized by having a processor and a memory for storing executable instructions of said processor, wherein said processor is configured to execute said executable instructions to perform a trajectory proximity inquiry method described in any one of claims 1 to 8 and claims 10 to 13. Claim 16 A computer-readable storage medium storing a computer program that implements a trajectory proximity lookup method described in any one of claims 1 through 8 and claims 10 through 13 when executed by a processor.

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