A convex hull analysis method and system for Internet of Things clusters

Abstract

The present invention discloses a convex hull analysis method and system for an Internet of Things cluster. The method obtains detection data of an Internet of Things cluster in multiple application scenarios, extracts the logical problem type corresponding to the detection data, constructs a convex hull structure of the Internet of Things cluster according to the logical problem type, determines the convex hull position relationship of the convex hull structure, constructs a first test problem of the convex hull structure according to the convex hull overlap and the logical problem type, and performs observation analysis on the first test problem to obtain an observation result. When the observation result determines that the convex hull position relationship is that the convex hulls do not intersect, a second test problem of the convex hull structure is constructed and convex hull calculation is performed to complete the convex hull analysis of the Internet of Things cluster. The method can delete a minimum number of Internet of Things devices in an industrial Internet of Things ecosystem and accurately cluster the Internet of Things devices. The method uses two target algorithms belonging to the P class, has a polynomial calculation complexity, ensures a high execution speed, and makes it suitable for real-time applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of Internet of Things data processing, and in particular relates to a convex hull analysis method and system for an Internet of Things cluster. Background Art

[0002] Simple and low-cost sensors with limited processing power have gained significant popularity, especially in industrial and commercial systems, and especially in Internet of Things (IoT) and Industrial IoT applications. These sensors are often used to detect specific conditions and environmental monitoring, such as patient health monitoring, early fire detection, or drone identification. One of the main advantages of these sensors is their low price and scalability, allowing for widespread deployment to create a precise network of data collection points. Sensors such as DHT11 and MQ-2 are well suited for simple and low-cost applications in IoT systems, providing reliable environmental data for temperature, humidity, and gas detection. These sensors are widely used in medical monitoring, industrial applications, and fire detection systems. For example, heart rate and blood oxygen sensors such as MAX30100 are used for real-time patient monitoring in healthcare systems. The system uses ESP8266 microcontrollers and Arduino boards to connect the sensors to the network for data transmission and processing. These components are well suited for large IoT projects, providing scalability to manage numerous sensors while maintaining low power consumption and efficient data communication.

[0003] Currently, in terms of IoT device detection, it is necessary to use the existing generated data of various IoT devices to find defective data. This problem is actually NP-hard, which means that there is no solution that can solve this problem in logical polynomial time. However, in an industrial IoT environment, industrial IoT devices have spread throughout the field of tracking drones, which requires extracting the geometric version of IoT device data and building an accurate and fast algorithm for it to prove that the geometric version of the problem is not NP-hard. Therefore, it is urgent to provide a convex hull analysis method and system for IoT clusters to ensure that it allows for widespread deployment and creation of an accurate data collection point network to solve the above-mentioned technical problems. Summary of the invention

[0004] In view of this, the present invention provides a convex hull analysis method and system for an Internet of Things cluster, which can delete a minimum number of Internet of Things devices in the industrial Internet of Things ecosystem and accurately cluster the Internet of Things devices. The two proposed target algorithms belong to the P class and have polynomial computational complexity, ensuring a high execution speed, making them suitable for real-time applications. The following technical solutions are specifically adopted to achieve this.

[0005] In a first aspect, the present invention provides a convex hull analysis method for an Internet of Things cluster, comprising the following steps:

[0006] Acquire detection data of an IoT cluster in multiple application scenarios, and extract logical problem types corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logical problem types include P problems, NP problems, NP-complete problems, and NP-hard problems;

[0007] Constructing a convex hull structure of the Internet of Things cluster according to the type of logical problem, and determining a convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness;

[0008] Constructing a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and performing observation analysis on the first test problem to obtain an observation result;

[0009] When the observation results determine that the convex hull position relationship is that the convex hulls do not intersect, a second test problem of the convex hull structure is constructed and the convex hull calculation is performed to complete the convex hull analysis of the Internet of Things cluster.

[0010] As a preferred embodiment of the above technical solution, the detection data of the IoT cluster in multiple application scenarios is obtained, including:

[0011] The detection problem of each IIoT device transmitting information to the base station is represented as a set of m binary devices , and consider a single sample generated at time t Data, where IIoT devices are spread in the environment of tracking drones. IIoT devices are represented by the symbols + and -, corresponding to the longitude and latitude of the moving autonomous vehicle, respectively. + represents positive devices and - represents negative devices.

[0012] The first fast sub-algorithm is used to prove the approximate value of the position of the drone, and the drone is outside the convex hull of the positive device and the negative device. The first fast sub-algorithm is:

[0013] set up Device sample values ​​and is the position of the target UAV at time t, and , , and are the convex hulls of A and B respectively, then , ;

[0014] The type of logic problem corresponding to the first fast sub-algorithm is an NP-hard problem, and a polynomial time algorithm is used to solve the NP-hard problem.

[0015] As a preferred embodiment of the above technical solution, extracting the logical problem type corresponding to the detection data includes:

[0016] Calculate the corresponding Almost 2-SAT problem according to the logic problem type, where the Almost 2-SAT problem includes a 2-CNF formula , integer k and whether it satisfies The problem of deleting at most k clauses in ;

[0017] The second fast subalgorithm is used to prove that the variable deletion Almost 2-SAT problem is Solve within time.

[0018] As a preferred embodiment of the above technical solution, the first test problem of the convex hull structure is constructed according to the convex hull overlap and the logic problem type, including:

[0019] The third fast sub-algorithm is used to prove the first test problem. The third fast sub-algorithm includes: assuming that P and Q are vertices of two convex polygons with n and m, and the 2D algorithm determines P and Q in intersect in time;

[0020] When the first test problem is applied to a binary sensor network and target tracking, the sensor network in the preset binary sensor does not work properly, and if the two convex hulls overlap, the sensor is making an error;

[0021] The first test problem consists of the minimum removal of symbols: there is a set of positive points on the plane and a set of negative points , if an integer , then judge Whether there are K points removed will be and Produces two disjoint convex hulls.

[0022] As a preferred embodiment of the above technical solution, observing and analyzing the first test problem to obtain an observation result includes:

[0023] If the two given points A and B in the first test problem, the minimum point to be deleted may be located at ;

[0024] Every pair of points lies on the convex hull if removing it would force the removal of all points between them;

[0025] The first test problem becomes simple if the area containing the plus or minus sign is known.

[0026] As a preferred embodiment of the above technical solution, a separating axis algorithm can be used to determine whether two convex polygons intersect. The separating axis algorithm includes:

[0027] There exists a line between two non-intersecting convex polygons, the line exists when the sides of one of the convex polygons form the line, and the point of the line closest to the other convex polygon is the point of the line closest to a corner of the one of the convex polygons;

[0028] The sides of one of the convex polygons will form a separating axis between the two convex polygons. If the two middle sides of the two convex polygons are parallel, then the two middle sides are the separating axis.

[0029] As a preferred embodiment of the above technical solution, a fourth fast sub-algorithm is used to summarize the observation results to obtain a hyperplane separation algorithm, including:

[0030] Let A and B be two disjoint nonempty convex subsets of , then there exists a nonzero vector v and a real number c such that all x in A are and all y in B are , to obtain the hyperplane , v is the normal vector, separating A and B;

[0031] According to every two point arrays on the plane and Compute the cost of each line segment consisting of a pair of points, select the pair with the lowest cost, and return the points that form the separating axis;

[0032] Determine a first target algorithm solution based on the minimum number of removed symbols for the first test problem in which the minimum removed symbol comprises a plus sign or a minus sign.

[0033] As a preferred embodiment of the above technical solution, the execution process of the first target algorithm includes:

[0034] use Solve the second test problem. If we plot the dual space of the second test problem, we see regions, among which and ;

[0035] Find the optimal cell unit in the dual space and one of the points , where the second test problem is to use the given point duality problem and prove that The duality of .

[0036] As a preferred embodiment of the above technical solution, a double line is drawn in the dual space for all given points in A and B, appearing in two colors. The segments and half-rows of the dual space are stored in the edge list of the connecting lines, where the edge list includes the color of each edge;

[0037] Build the floor plan ,vertex The starting cell assigned is the cell above the upper envelope, the vertex Assign to target cells in any order, wherein the target cells are cells other than the starting cell and the cells above the upper envelope;

[0038] If two vertices are adjacent, there is an edge between the two vertices. E contains all the edges between every two adjacent vertices. The generated graph has vertices and edges, each vertex and edge is processed once;

[0039] Calculate a pair of numbers and As the weight of the vertex, set and , set the weights of adjacent vertices according to the line segments between the vertices, and use the queue structure to calculate the weights of all vertices, where The weighted plan graph can be calculated in time;

[0040] If the separator line is a double line at vertex v, delete Plus sign and minus sign, and adopt the second target algorithm in Use within time and lines in the line collection Find the optimal vertex , wherein the second objective algorithm includes assuming A and B are two sets of points in a plane, and , according to the second objective algorithm, find the minimum number of removed points so that There are two disjoint convex hulls in .

[0041] In a second aspect, the present invention further provides a convex hull analysis system for an Internet of Things cluster, which is applied to the convex hull analysis method for the Internet of Things cluster, comprising:

[0042] A detection data acquisition module, used to acquire detection data of an IoT cluster in multiple application scenarios, and extract the logic problem type corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logic problem types include P problems, NP problems, NP-complete problems, and NP-hard problems;

[0043] A convex hull structure construction module, used to construct a convex hull structure of the Internet of Things cluster according to the type of logical problem, and determine the convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness;

[0044] A test problem construction module, used to construct a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and perform observation analysis on the first test problem to obtain an observation result;

[0045] The convex hull analysis module is used to construct a second test problem of the convex hull structure and perform convex hull calculation to complete the convex hull analysis of the Internet of Things cluster when the observation results determine that the convex hull position relationship is that the convex hulls do not intersect.

[0046] The present invention provides a convex hull analysis method and system for an Internet of Things cluster. The method obtains detection data of an Internet of Things cluster in multiple application scenarios, extracts the logical problem type corresponding to the detection data, constructs a convex hull structure of the Internet of Things cluster according to the logical problem type, determines the convex hull position relationship of the convex hull structure, constructs a first test problem of the convex hull structure according to the convex hull overlap and the logical problem type, and performs observation analysis on the first test problem to obtain an observation result. When the observation result determines that the convex hull position relationship is that the convex hulls do not intersect, a second test problem of the convex hull structure is constructed and convex hull calculation is performed to complete the convex hull analysis of the Internet of Things cluster. The method can delete a minimum number of Internet of Things devices in an industrial Internet of Things ecosystem and accurately cluster the Internet of Things devices. The method uses two target algorithms belonging to the P class, has a polynomial calculation complexity, ensures a high execution speed, and makes it suitable for real-time applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0048] Figure 1 A flow chart of the convex hull analysis method for the Internet of Things cluster provided by the present invention;

[0049] Figure 2 A structural block diagram of the convex hull analysis system for the Internet of Things cluster provided by the present invention;

[0050] Figure 3 A schematic diagram of convex hull overlap formed by devices in the IIoT ecosystem provided by the present invention;

[0051] Figure 4 A schematic diagram of a first observation result provided by the present invention;

[0052] Figure 5 A schematic diagram of a second observation result provided by the present invention;

[0053] Figure 6 A schematic diagram of a third observation result provided by the present invention;

[0054] Figure 7 A schematic diagram of the splitting axes of the two convex hulls provided by the present invention;

[0055] Figure 8 A schematic diagram of the dual space provided by the present invention;

[0056] Fig. 9 Plan view provided for the present invention Vertex Segmented schematic diagram;

[0057] Fig.10 The E provided by the present invention includes a schematic diagram of the edge between two adjacent vertices;

[0058] Fig.11 for Figure 8 A schematic diagram of the dual plane. DETAILED DESCRIPTION

[0059] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0060] See also Figure 1 The present invention provides a convex hull analysis method for an Internet of Things cluster, comprising the following steps:

[0061] S1: Acquire detection data of an IoT cluster in multiple application scenarios, and extract logical problem types corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logical problem types include P problems, NP problems, NP-complete problems, and NP-hard problems;

[0062] S2: constructing a convex hull structure of the IoT cluster according to the type of the logic problem, and determining a convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness;

[0063] S3: constructing a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and performing observation analysis on the first test problem to obtain an observation result;

[0064] S4: When the observation results determine that the convex hull position relationship is that the convex hulls do not intersect, a second test problem of the convex hull structure is constructed and the convex hull calculation is performed to complete the convex hull analysis of the Internet of Things cluster.

[0065] In this embodiment, there are two IIoT devices, and two convex hulls have been created. These convex hulls overlap, which has a bad impact on the clustering problem of IIoT devices, because different sensing aspects can be applied to various targets such as temperature, light, sound, etc., and devices that only generate one bit of information at a time can provide communication. The purpose is to reduce the minimum number of IIoT devices, so that you can have a convex hull without overlapping forging, so as to achieve accurate clustering. NP-hard problems (NP-hard) are those that are at least as difficult as the hardest problems in NP. In computational complexity theory, if every problem L that can be solved in non-deterministic polynomial time can be reduced to problem H in polynomial time, then problem H is called an NP-hard problem; if a polynomial time algorithm can be found to solve a single NP-hard problem, then a polynomial time algorithm can be found for all problems in NP. Since P≠NP is generally suspected, it is likely that there is no polynomial time algorithm for NP-hard problems. There are some fundamental problems in computational complexity that are NP-hard, and while the 2-SAT problem belongs to the P class, some versions like "Max 2-SAT", "Almost 2-SAT", and "Variable-Removed Almost 2-SAT" are NP-hard, and are referred to in theoretical computer science as Almost 2-SAT. Among them, this invention proves that when the problem is confined to geometric data, it is no longer computationally difficult to solve and can be solved with a polynomial-time algorithm.

[0066] It should be noted that if Figure 3 As shown in Figure 1, an Industrial IoT environment where IIoT devices have a distribution in the field of tracking drones. IIoT devices are represented by + and - symbols, which represent the longitude and latitude of the moving autonomous car. Two convex hulls. Due to the presence of two IIoT devices, these convex hulls overlap, which also has a negative impact on the IIoT device clustering problem. Generally speaking, they do not have much complexity in different sensing modalities. These aspects can be applied to various targets in these systems such as temperature, light, sound, etc. Each result only generates one bit of information and provides cheap communication. The goal is to reduce the minimum number of IIoT devices so that it is possible to have a convex hull, constructed without overlap, with accurate clustering. Low-cost sensors and wireless networks play a vital role in healthcare systems, especially for real-time positioning and tracking of patients and medical equipment. These technologies have significant advantages in large hospitals and clinics, where efficient resource management and patient monitoring are essential. By deploying sensors or wireless tags, healthcare providers can track the movement of patients within the facility, ensuring timely intervention when needed. For example, patients with Alzheimer's disease can be monitored and located. In addition, these systems are used to track basic equipment such as beds, oxygen tanks, and wheelchairs. By leveraging low-cost sensors, healthcare organizations can gain new efficiencies, particularly in managing the flow of patients and medical assets in real time.

[0067] It should be understood that by acquiring detection data of the Internet of Things cluster in multiple application scenarios and extracting the logical problem type corresponding to the detection data, the convex hull structure of the Internet of Things cluster is constructed according to the logical problem type, and the convex hull position relationship of the convex hull structure is determined, and the first test problem of the convex hull structure is constructed according to the convex hull overlap and the logical problem type, and the first test problem is observed and analyzed to obtain an observation result. When the observation result determines that the convex hull position relationship is that the convex hulls do not intersect, a second test problem of the convex hull structure is constructed and a convex hull calculation is performed to complete the convex hull analysis of the Internet of Things cluster. The minimum number of Internet of Things devices can be deleted in the industrial Internet of Things ecosystem, and the Internet of Things devices can be accurately clustered. The two target algorithms belong to the P class and have a polynomial calculation complexity, which ensures a high execution speed, making it suitable for real-time applications.

[0068] Optionally, detection data of the IoT cluster in multiple application scenarios is obtained, including:

[0069] The detection problem of each IIoT device transmitting information to the base station is represented as a set of m binary devices , and consider a single sample generated at time t Data, where IIoT devices are spread in the environment of tracking drones. IIoT devices are represented by the symbols + and -, corresponding to the longitude and latitude of the moving autonomous vehicle, respectively. + represents positive devices and - represents negative devices.

[0070] The first fast sub-algorithm is used to prove the approximate value of the position of the drone, and the drone is outside the convex hull of the positive device and the negative device. The first fast sub-algorithm is:

[0071] set up Device sample values ​​and is the position of the target UAV at time t, and , , and are the convex hulls of A and B respectively, then , ;

[0072] The type of logic problem corresponding to the first fast sub-algorithm is an NP-hard problem, and a polynomial time algorithm is used to solve the NP-hard problem.

[0073] In this embodiment, extracting the logic problem type corresponding to the detection data includes: calculating the corresponding Almost 2-SAT problem according to the logic problem type, wherein the Almost 2-SAT problem includes a 2-CNF formula , integer k and whether it satisfies The problem of deleting at most k clauses in ; the second fast subalgorithm is used to prove that the variable deletion Almost 2-SAT problem is In other words, in the variable deletion Almost 2-SAT (variable deletion variant), at most k variables are allowed to be detected, each variable and all clauses containing it are deleted, and deleting a variable can be regarded as setting it to true and false at the same time.

[0074] Optionally, constructing a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type includes:

[0075] The third fast sub-algorithm is used to prove the first test problem. The third fast sub-algorithm includes: assuming that P and Q are vertices of two convex polygons with n and m, and the 2D algorithm determines P and Q in intersect in time;

[0076] When the first test problem is applied to a binary sensor network and target tracking, the sensor network in the preset binary sensor does not work properly, and if the two convex hulls overlap, the sensor is making an error;

[0077] The first test problem consists of the minimum removal of symbols: there is a set of positive points on the plane and a set of negative points , if an integer , then judge Whether there are K points removed will be and Produces two disjoint convex hulls.

[0078] In this embodiment, observing and analyzing the first test question to obtain an observation result includes:

[0079] If the two given points A and B in the first test problem, the minimum point to be deleted may be located at ;

[0080] Every pair of points lies on the convex hull if removing each pair of points on the convex hull would force the removal of all points between the pair of points;

[0081] The first test problem becomes simple if the area containing the plus or minus sign is known.

[0082] In this embodiment, to determine whether two convex polygons intersect, the separating axis theorem can be used. For two non-intersecting convex polygons, there is a line between them. Obviously, such a line exists if and only if the edge of one of the polygons forms the line. The point of this line closest to the other polygon is the point closest to a corner of the first polygon (such as Figure 7). This edge will then form a separating axis between the polygons. If the two middle edges of two polygons are parallel, they are both separating axes.

[0083] Optionally, a separating axis algorithm may be used to determine whether two convex polygons intersect, the separating axis algorithm comprising:

[0084] There exists a line between two non-intersecting convex polygons, the line exists when the sides of one of the convex polygons form the line, and the point of the line closest to the other convex polygon is the point of the line closest to a corner of the one of the convex polygons;

[0085] The sides of one of the convex polygons will form a separating axis between the two convex polygons. If the two middle sides of the two convex polygons are parallel, then the two middle sides are the separating axis.

[0086] In this embodiment, the fourth fast sub-algorithm is used to summarize the observation results to obtain a hyperplane separation algorithm, including: assuming that A and B are two disjoint nonempty convex subsets of , then there exists a nonzero vector v and a real number c such that all x in A are and all y in B are , to obtain the hyperplane , v is the normal vector, separating A and B; according to the array of every two points on the plane and Calculate the cost of each line segment composed of a pair of points, select the pair with the minimum cost, and return the points that constitute the separating axis; determine the first target algorithm solution based on the minimum number of removed symbols for the first test problem in which the minimum removed symbol comprises a plus sign or a minus sign.

[0087] Optionally, the execution process of the first target algorithm includes:

[0088] use Solve the second test problem. If we plot the dual space of the second test problem, we see regions, among which and ;

[0089] Find the optimal cell unit in the dual space and one of the points , where the second test problem is to use the given point duality problem and prove that The duality of .

[0090] In this example, a double line is drawn in the dual space for all given points in A and B, appearing in two colors. segments and half-rows, the dual space is stored in the edge list of the connecting line, where the edge list includes the color of each edge; construct the planar graph ,vertex The starting cell assigned is the cell above the upper envelope, the vertex Assign to the target cell in any order, where the target cell is the cell other than the starting cell and the cell above the upper envelope; if two vertices are adjacent, there is an edge between the two vertices, E contains all the edges between every two adjacent vertices, and the generated graph has vertices and edges, processing each vertex and edge once; calculate a pair of numbers and As the weight of the vertex, set and , set the weights of adjacent vertices according to the line segments between the vertices, and use the queue structure to calculate the weights of all vertices, where The weighted planar graph can be calculated in time; if the separator is a double line of vertex v, then delete Plus sign and minus sign, and adopt the second target algorithm in Use within time and lines in the line collection Find the optimal vertex , wherein the second objective algorithm includes assuming A and B are two sets of points in a plane, and , according to the second objective algorithm, find the minimum number of removed points so that There are two disjoint convex hulls in .

[0091] Specifically, we introduce a new problem related to convex hull, applicable to shape modeling and IIoT environments, solve it in polynomial time, and as a consequence, propose a naive The algorithm is the first target algorithm. In order to solve this problem, a new solution algorithm is proposed: As mentioned before, this problem is similar to a version of the 2-SAT problem. One of the most important applications of detecting and testing intersections between objects is computing geometric figures in the network domain. This problem has many applications in text mining and other NLP (natural language processing) that require the separation of a given dataset into some disjoint subsets. The first application of plane sweeping techniques has raised the importance of finding efficient algorithms for intersection testing or collision detection, as this type of problem has many applications in robotics, computer graphics, computer-aided design, and VLSI design.

[0092] Specifically, the first test problem appears to be NP-hard and is structurally very similar to the variable-elimination Almost 2-SAT problem. However, due to some geometric reasons, this problem can be solved in polynomial time, which can be easily considered by the following three observations about two disjoint convex hulls of given points in the 2D plane. The first observation is that for two given sets of points A and B in Problem 1, the minimum point that should be removed may be located at ,like Figure 4 The second observation is that removing every pair of points on the convex hull forces the removal of all points between them (either clockwise or counterclockwise) that lie on the convex hull, as Figure 5 As shown; the third observation is that if we know the area containing only plus (minus) signs, the problem may become simpler, such as Figure 6 As shown. Among them, Figure 5 In the figure, deleting points a and d will force deletion or ; Figure 6 All sensors in region A (B) are positive (negative) and can only be removed from region C.

[0093] Specifically, for the problem of using given point duality, a new fast algorithm, the second objective algorithm, is proposed, such as Figure 8 As shown, if we plot the dual space, we see To find the optimal line in the primal space, find an optimal cell unit and a point in the dual space. , Proved The duality of Figure 8 The red dot in and blue dots .in, The execution process of the algorithm includes:

[0094] First, draw the dual lines for all given points in A (plus) and B (minus) in the dual space, with red and blue assigned to the dual lines of sets A and B, respectively. segments and half-rows. The dual spaces are stored in doubly connected edge lists (DCELs), where the edge lists also contain the color of each edge. This process requires At this point, the floor plan can be generated as follows .vertex The starting cell assigned is the cell above the upper envelope (e.g. Fig. 9 ).vertex to every other cell in any order. If two vertices are adjacent, there is an edge between them, so E contains all the edges (line 6) between every two adjacent vertices (as Fig.10 ), the generated graph has vertices and edges, processing each vertex and edge once.

[0095] like Fig.10 As shown, each cell is labeled in any order, and there is an edge between two vertices only if the cells corresponding to them are adjacent. Fig.11 As shown, Fig.11 yes Figure 8 The dual plane, dual points (lines) and a black dot are located in the region that separates the blue and red lines with the minimum error (only and is on the wrong side of the black dot). The next step is to calculate a pair of numbers and As the weight of the vertex: First, set and , then set the weights of adjacent vertices based on the line segment between them, so that if the line segment is red, then reduce Without changing , if the line segment is blue, then reduce And keep unchanged, so for each vertex v, and denotes the number of red lines below v and the number of blue lines above v, respectively. Using the queue structure Q, the weights of all vertices are calculated. At each step, when an unweighted vertex appears by crossing the red (blue) segment, Decrease (increase) by 1. Computing the weight of a new vertex takes constant time; therefore, time, we can compute a weighted planar graph where the weights and The red line below and the blue line above the cell containing vertex v are shown. When applying and finding two disjoint convex hulls in sensor networks, if the separating line is a double line of vertex v, it should be removed Plus sign and Minus. The second objective algorithm is Use within time and Line Find the optimal vertex , all the results in the second objective algorithm can be obtained.

[0096] See also Figure 2 The present invention also provides a convex hull analysis system for an Internet of Things cluster, which is applied to the convex hull analysis method for the Internet of Things cluster, and includes:

[0097] A detection data acquisition module, used to acquire detection data of an IoT cluster in multiple application scenarios, and extract the logic problem type corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logic problem types include P problems, NP problems, NP-complete problems, and NP-hard problems;

[0098] A convex hull structure construction module, used to construct a convex hull structure of the Internet of Things cluster according to the type of logical problem, and determine the convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness;

[0099] A test problem construction module, used to construct a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and perform observation analysis on the first test problem to obtain an observation result;

[0100] The convex hull analysis module is used to construct a second test problem of the convex hull structure and perform convex hull calculation to complete the convex hull analysis of the Internet of Things cluster when the observation results determine that the convex hull position relationship is that the convex hulls do not intersect.

[0101] In this example, the problem of accurate clustering in an industrial IoT environment is solved by solving the major challenge of the “Almost 2-SAT” problem. First, it is depicted in a geometric environment. Then, the problem is solved by two different algorithms, and the first target algorithm is a naive but slower method with a time complexity of However, the second objective algorithm uses the dual space and has a time complexity of And it is faster. In addition to the mathematical proof, the effectiveness in the industrial IoT environment is also demonstrated, which can remove the minimum number of IoT devices in the industrial IoT ecosystem and accurately cluster the IoT devices. The two algorithms proposed in this paper belong to the P class and have polynomial computational complexity, which ensures a high execution speed and makes them suitable for real-time applications.

[0102] In all examples shown and described herein, any specific values ​​should be interpreted as merely exemplary and not as limiting, and thus other examples of the exemplary embodiments may have different values.

[0103] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0104] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A convex hull analysis method for an Internet of Things cluster, characterized in that: The following steps are involved: Acquire detection data of an IoT cluster in multiple application scenarios, and extract logical problem types corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logical problem types include P problems, NP problems, NP-complete problems, and NP-hard problems; Constructing a convex hull structure of the Internet of Things cluster according to the type of logical problem, and determining a convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness; Constructing a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and performing observation analysis on the first test problem to obtain an observation result; When the observation results determine that the convex hull position relationship is that the convex hulls do not intersect, construct a second test problem of the convex hull structure and perform convex hull calculation to complete the convex hull analysis of the Internet of Things cluster; Obtain detection data for IoT clusters in multiple application scenarios, including: The detection problem of each IIoT device transmitting information to the base station is represented as a set of m binary devices , and consider a single sample generated at time t Data, where IIoT devices are spread in the environment of tracking drones. IIoT devices are represented by the symbols + and -, corresponding to the longitude and latitude of the moving autonomous vehicle, respectively. + represents positive devices and - represents negative devices. The first fast sub-algorithm is used to prove the approximate value of the position of the drone, and the drone is outside the convex hull of the positive device and the negative device. The first fast sub-algorithm is: set up Device sample values ​​and is the position of the target UAV at time t, and , , and are the convex hulls of A and B respectively, then , ; The type of logic problem corresponding to the first fast sub-algorithm is an NP-hard problem, and a polynomial time algorithm is used to solve the NP-hard problem.

2. The convex hull analysis method of the Internet of Things cluster according to claim 1 is characterized in that: Extracting the logical problem type corresponding to the detection data includes: Calculate the corresponding Almost 2-SAT problem according to the logic problem type, where the Almost 2-SAT problem includes a 2-CNF formula , integer k and whether it satisfies The problem of deleting at most k clauses in ; The second fast subalgorithm is used to prove that the variable deletion Almost 2-SAT problem is Solve within time.

3. The convex hull analysis method of the Internet of Things cluster according to claim 1 is characterized in that: Constructing a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, comprising: The third fast sub-algorithm is used to prove the first test problem. The third fast sub-algorithm includes: assuming that P and Q are vertices of two convex polygons with n and m, and the 2D algorithm determines P and Q in intersect in time; When the first test problem is applied to a binary sensor network and target tracking, the sensor network in the preset binary sensor does not work properly, and if the two convex hulls overlap, the sensor is making an error; The first test problem consists of the minimum removal of symbols: there is a set of positive points on the plane and a set of negative points , if an integer , then judge Whether there are K points removed will be and Produces two disjoint convex hulls.

4. The convex hull analysis method of the Internet of Things cluster according to claim 3 is characterized in that: Observation analysis is performed on the first test question to obtain observation results, including: If the two given points A and B in the first test problem, the minimum point to be deleted may be located at ; Every pair of points lies on the convex hull if removing each pair of points on the convex hull would force the removal of all points between the pair of points; The first test problem becomes simple if the area containing the plus or minus sign is known.

5. The convex hull analysis method of the Internet of Things cluster according to claim 4 is characterized in that: A separating axis algorithm may be used to determine whether two convex polygons intersect, and the separating axis algorithm includes: There exists a line between two non-intersecting convex polygons, the line exists when the sides of one of the convex polygons form the line, and the point of the line closest to the other convex polygon is the point of the line closest to a corner of the one of the convex polygons; The sides of one of the convex polygons will form a separating axis between the two convex polygons. If the two middle sides of the two convex polygons are parallel, then the two middle sides are the separating axis.

6. The convex hull analysis method of the Internet of Things cluster according to claim 5, characterized in that: The fourth fast sub-algorithm is used to summarize the observation results to obtain a hyperplane separation algorithm, including: Let A and B be two disjoint nonempty convex subsets of , then there exists a nonzero vector v and a real number c such that all x in A are and all y in B are , to obtain the hyperplane , v is the normal vector, separating A and B; According to every two point arrays on the plane and Compute the cost of each line segment consisting of a pair of points, select the pair with the lowest cost, and return the points that form the separating axis; Determine a first target algorithm solution based on the minimum number of removed symbols for the first test problem in which the minimum removed symbol comprises a plus sign or a minus sign.

7. The convex hull analysis method of the Internet of Things cluster according to claim 6, characterized in that: The execution process of the first target algorithm includes: use Solve the second test problem. If we plot the dual space of the second test problem, we see regions, among which and ; Find the optimal cell unit in the dual space and one of the points , where the second test problem is to use the given point duality problem and prove that The duality of .

8. The convex hull analysis method of the Internet of Things cluster according to claim 7, characterized in that: Also includes: Draw double lines in the dual space for all given points in A and B, appearing in two colors The segments and half-rows of the dual space are stored in the edge list of the connecting lines, where the edge list includes the color of each edge; Build the floor plan ,vertex The starting cell assigned is the cell above the upper envelope, the vertex Assign to target cells in any order, wherein the target cells are cells other than the starting cell and the cells above the upper envelope; If two vertices are adjacent, there is an edge between the two vertices. E contains all the edges between every two adjacent vertices. The generated graph has vertices and edges, each vertex and edge is processed once; Calculate a pair of numbers and As the weight of the vertex, set and , set the weights of adjacent vertices according to the line segments between the vertices, and use the queue structure to calculate the weights of all vertices, where The weighted plan graph can be calculated in time; If the separator is a double line at vertex v, delete Plus sign and minus sign, and adopt the second target algorithm in Use within time and lines in the line collection Find the optimal vertex , wherein the second objective algorithm includes assuming A and B are two sets of points in a plane, and , according to the second objective algorithm, find the minimum number of removed points so that There are two disjoint convex hulls in .

9. A convex hull analysis system for an Internet of Things cluster, characterized in that: The convex hull analysis method applied to the Internet of Things cluster as claimed in any one of claims 1 to 8 comprises: A detection data acquisition module, used to acquire detection data of an IoT cluster in multiple application scenarios, and extract the logic problem type corresponding to the detection data, wherein the IoT cluster includes sensors, binary devices, self-driving cars, IIoT devices, and tracking drones, and the logic problem types include P problems, NP problems, NP-complete problems, and NP-hard problems; A convex hull structure construction module, used to construct a convex hull structure of the Internet of Things cluster according to the type of logical problem, and determine the convex hull position relationship of the convex hull structure, wherein the convex hull position relationship includes convex hull overlap and convex hull disjointness; A test problem construction module, used to construct a first test problem of the convex hull structure according to the convex hull overlap and the logic problem type, and perform observation analysis on the first test problem to obtain an observation result; The convex hull analysis module is used to construct a second test problem of the convex hull structure and perform convex hull calculation to complete the convex hull analysis of the Internet of Things cluster when the observation results determine that the convex hull position relationship is that the convex hulls do not intersect.

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