Apparatus and method for embedding search paths with dynamic resolution-based geospace
By segmenting a large road network into multiple blocks and using a dynamic resolution ETA prediction model, the problem of inaccurate ETA prediction in the prior art is solved, and more accurate path search and resource conservation are achieved.
Patent Information
- Application Number
- CN202411656429.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-11-21
- Filing Date
- 2024-11-19
- Publication Date
- 2025-05-23
AI Technical Summary
When using the entire road network, the prior art is difficult to incorporate into the actual road environment, resulting in inaccurate ETA predictions and affecting the effect of path search.
By segmenting a large road network into multiple blocks based on dynamic resolution, the segmented network is used to train and search the ETA prediction model.
Through dynamic resolution road network segmentation, ETA can be predicted more accurately, reducing the use of computer resources, and improving the efficiency of path search.
Smart Images

Figure CN120027806A_ABST
Abstract
Description
Technical Field
[0001] Exemplary embodiments of the present disclosure relate to an apparatus and method for searching a path using geospatial embedding based on dynamic resolution, and more particularly, to a path search apparatus and method for performing a path search by segmenting a large road network based on dynamic resolution and using the segmented network to predict an estimated time of arrival (ETA). Background Art
[0002] Recently, most vehicles are equipped with navigation devices. In addition, due to the increase in vehicles, traffic jams often occur on roads and intersections. Therefore, although the user travels on a known road, the user usually performs a route search through navigation to obtain guidance to check and avoid sections where traffic jams occur, such as roads or intersections.
[0003] Furthermore, when performing a route search, the user basically uses the estimated time of arrival (ETA) information. For example, the user determines the departure time or specifies the time based on the ETA information. Therefore, if the ETA is inaccurate, the user determines the departure time or specifies the time by further adding the floating time, and if the ETA is accurate, the floating time is reduced, allowing the user to save time without wasting time on the road.
[0004] Therefore, in the route search process using navigation, the optimal route and the recommended route are calculated by using the ETA.
[0005] With the development of deep learning-based information prediction technology, research on deep learning-based technology for more accurate ETA prediction is being actively conducted.
[0006] However, the prior art has a problem in that when the entire road network (eg, national road network) is used, the actual road environment is not incorporated, such as representing a country by cutting the country at predetermined intervals, or dividing the country for each administrative district. Summary of the invention
[0007] Various embodiments are directed to providing an apparatus and method for searching a path using geospatial embedding based on dynamic resolution, which segments a large road network based on dynamic resolution so that the actual road environment can be incorporated.
[0008] In an embodiment, an apparatus for searching a route using geospatial embedding based on dynamic resolution includes a storage module and a processor, the storage module being configured to store digital map data, the processor being configured to perform a route search based on an estimated time of arrival (ETA) prediction model in response to a route search request, the ETA prediction model being based on a road network segmented into a plurality of blocks.
[0009] In an embodiment of the present disclosure, the ETA prediction model is based on a road network that is divided into a plurality of blocks by a plurality of links merging into the road.
[0010] In an embodiment of the present disclosure, the ETA prediction model is based on a road network that is segmented into a plurality of blocks according to the maximum number of links that can be included in one block.
[0011] In an embodiment of the present disclosure, the ETA prediction model is based on a tree expanded by inserting all links of a road network into a block and dividing the block into a preset number when the number of links inserted into one block is greater than a maximum number of links.
[0012] In an embodiment of the present disclosure, the ETA prediction model is based on link information that is split and stored in a leaf node when the tree becomes a leaf node that is no longer expanded.
[0013] In an embodiment of the present disclosure, the ETA prediction model is based on identifier information (ID information) assigned to each of the finally segmented untree-no longer-extended blocks.
[0014] In an embodiment of the present disclosure, the ETA prediction model uses ID information of a block including a link according to a path search as an input value.
[0015] In an embodiment of the present disclosure, the processor calculates a plurality of candidate paths in response to a path search request, and calculates the ETA of each candidate path through an ETA prediction model.
[0016] In an embodiment of the present disclosure, the processor calculates the cost of each candidate path based on the calculated ETA of each candidate path.
[0017] In an embodiment, a method for generating an ETA prediction model includes inserting, by a processor, road links of a road network into a tree, expanding, by the processor, the tree by splitting the block into a preset number when the number of links in the block inserted into the tree is greater than the maximum number of links that can be included in one block, assigning, by the processor, ID information to each block in the block that has finally been split into blocks that are no longer expanded, and training the ETA prediction model by the processor using the ID information of the block as an input value, the block including links of a path predicted according to the ETA.
[0018] In an embodiment of the present disclosure, in the training of the ETA prediction model, the processor trains the ETA prediction model by further using dynamic features including time information and traffic features including traffic speed information of links as input values.
[0019] In an embodiment of the present disclosure, the ETA prediction model outputs the link transit time as an output value.
[0020] In an embodiment of the present disclosure, the ETA prediction model outputs the ETA of all paths as output values.
[0021] In an embodiment, a method for searching a route using geospatial embedding based on dynamic resolution includes: receiving a route search request by a processor, performing a route search based on an estimated time of arrival (ETA) prediction model by the processor, and providing a result of the route search by the processor. The ETA prediction model is based on a road network segmented into a plurality of blocks.
[0022] In an embodiment of the present disclosure, performing a path search includes calculating, by a processor, a plurality of candidate paths in response to a path search request, and calculating, by the processor, an ETA of each candidate path by using an ETA prediction model.
[0023] In an embodiment of the present disclosure, performing the path search further includes calculating, by the processor, a cost of each candidate path based on the calculated ETA of each candidate path.
[0024] In an embodiment of the present disclosure, the method further includes, before receiving the path search request, training, by the processor, an ETA prediction model by using ID information of a block as an input value, the block including links of the path predicted according to the ETA.
[0025] In an embodiment of the present disclosure, the ETA prediction model is based on a road network that is segmented into a plurality of blocks according to the maximum number of links that can be included in one block.
[0026] In an embodiment of the present disclosure, the ETA prediction model is based on a tree that is expanded by inserting all links of a road network into a block and dividing the block into a preset number when the number of links inserted into one block is greater than a maximum number of links.
[0027] In an embodiment of the present disclosure, the ETA prediction model is based on link information that is split and stored in a leaf node when the tree becomes a leaf node that is no longer expanded.
[0028] The apparatus and method for searching a path using geospatial embedding based on dynamic resolution according to an embodiment of the present disclosure has the effect that, since a road network is divided into a plurality of blocks based on dynamic resolution, computer resources can be reduced by reducing unnecessary use of data. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] Figure 1 is an exemplary diagram showing a schematic construction of an apparatus for embedding a search path using geospatial information based on dynamic resolution according to an embodiment of the present disclosure.
[0030] Figure 2The invention is a flowchart for describing geospatial embedding based on dynamic resolution in an apparatus for searching a path using geospatial embedding based on dynamic resolution according to an embodiment of the present disclosure.
[0031] Figure 3 It is an example diagram for describing a dynamic block segmentation method in an apparatus for embedding a search path using a geospatial method based on dynamic resolution according to an embodiment of the present disclosure.
[0032] Figure 4 is an example diagram for describing a static block segmentation method for path search.
[0033] Figure 5 is an example diagram for describing an ETA prediction model of an apparatus for using a dynamic-resolution-based geospatial embedded search path according to an embodiment of the present disclosure.
[0034] Figure 6 The invention is a flowchart for describing a method of using geospatial embedding search paths based on dynamic resolution according to an embodiment of the present disclosure.
[0035] Figure 7 is a flowchart for describing the use of an ETA prediction model in a method of using a dynamic-resolution-based geospatial embedded search path according to an embodiment of the present disclosure. DETAILED DESCRIPTION
[0036] In the following, an apparatus and method for embedding a search path using geospatial information based on dynamic resolution according to an embodiment of the present disclosure are described with reference to the accompanying drawings. In the process, for the sake of clarity and convenience of description, the thickness of the line segments or the size of the components shown in the accompanying drawings may have been exaggerated. The terms to be described below are defined by considering their functions in the present disclosure and may change according to the intention or practice of the user or operator. Therefore, these terms should be defined according to the overall content of this specification.
[0037] Figure 1 is an exemplary diagram showing a schematic construction of an apparatus for embedding a search path using geospatial information based on dynamic resolution according to an embodiment of the present disclosure.
[0038] like Figure 1 As shown, the apparatus for searching a path using geospatial embedding based on dynamic resolution according to the present embodiment includes a global positioning system (GPS) module 110 , a storage module 120 , a processor 130 and a communication module 140 .
[0039] The GPS module 110 receives a GPS signal for detecting a current location of a vehicle, and also receives information on a current location of a navigation device by using the GPS module.
[0040] In addition, although not shown, the GPS module 110 may receive traffic (or traffic volume) information and vehicle traffic information for each link, lane information for each road, and traffic condition information (e.g., accidents, incidents, or construction) through a real-time traffic information receiving module (not shown) or the communication module 140.
[0041] The internal memory (or database) of the processor 130 (not shown) stores digital map data (e.g., precise map data and high-definition (HD) maps). The digital map data includes geographical coordinates representing latitude and longitude in degrees / minutes / seconds.
[0042] The storage module 120 stores link information based on the digital map data and may store the traffic information history for each link received through the communication module 140.
[0043] The storage module 120 may store the real-time traffic information history for each link by season, by day, and by hour.
[0044] In this case, the storage module 120 may store the real-time traffic information history for each link in the server 200 when operating in cooperation with the server 200, or may also store the real-time traffic information history within a predetermined period (e.g., a specified predetermined period) (e.g., one year).
[0045] Therefore, hereinafter, the information stored in the storage module 120 should be understood as a concept that even includes the information stored in the server 200.
[0046] The processor 130 may perform learning (e.g., deep learning) by incorporating the information stored in the storage module 120 (e.g., the real-time traffic information for each link and information on the attributes of the road (e.g., the number of lanes, the presence of signals, the number of turns, the collection trajectory, and the traffic information history)).
[0047] The processor 130 may include a path search engine (e.g., a path search algorithm) and an ETA prediction model (e.g., a deep learning model for ETA prediction).
[0048] The processor 130 may calculate (or compute) multiple candidate paths through the path search engine and may calculate (or compute) the optimal path among the candidate paths through the ETA prediction model.
[0049] When performing path search using an ETA prediction model based on dynamic resolution geospatial embedding, the processor 130 may calculate a more accurate best path.
[0050] The communication module 140 communicates with the server 200 (eg, an ETA prediction server, a cloud server, or a navigation server).
[0051] The device for searching a path using geospatial embedding based on dynamic resolution according to the present embodiment is a concept including a navigation terminal (not shown) installed in a vehicle and at least one external server 200 (e.g., a navigation server, a cloud server, or an estimated arrival time prediction server) connected to the navigation terminal (not shown) via communication.
[0052] For example, the device for searching the best path based on all paths according to the present embodiment can calculate a plurality of candidate paths by using at least one piece of information (e.g., real-time traffic information, ETA prediction information, and cost information) provided to the server 200 in a state where the best path search device based on all paths has been connected to the server 200 through communication or at least one piece of information (e.g., real-time traffic information, ETA prediction information, cost information) provided by the server 200, and calculate (or operate) the best path (i.e., the best candidate path with the minimum cost) among the plurality of candidate paths, thereby providing guidance.
[0053] Alternatively, in some embodiments, the device according to the present embodiment may be constructed in such a form that the server 200 receives a path search request from a navigation terminal installed in a vehicle, calculates an optimal path that has been incorporated into the ETA of all paths, and provides the optimal path to the navigation terminal.
[0054] In addition, the server 200 is equipped with a computing device such as a processor, and performs such a path search operation. Therefore, the operation of the server 200 can also be described as being performed by the processor.
[0055] The ETA prediction model generates a dimensional tree (the dimensional tree is obtained by dividing the road network into road link units), subdivides the dimensional tree, and then uses the value of the corresponding dimensional tree as a geospatial feature value through embedding. When a large road network is represented as described above, the limitation of unnecessary geographic representation can be overcome, and a more refined road network can be represented by dynamically representing only roads.
[0056] Figure 2 The invention is a flowchart for describing geospatial embedding based on dynamic resolution in an apparatus for searching a path using geospatial embedding based on dynamic resolution according to an embodiment of the present disclosure. Figure 3 It is an example diagram for describing a dynamic block segmentation method in an apparatus for embedding a search path using a geospatial method based on dynamic resolution according to an embodiment of the present disclosure. Figure 4 is an example diagram for describing a static block segmentation method for path search.
[0057] Reference Figure 2 First, a standard for dynamic geospatial embedding is set (S100). That is, in dynamic geospatial embedding (e.g., a block segmentation method or a road network segmentation algorithm based on dynamic resolution), the maximum number of links (e.g., 500) per block (or may also be represented as a unit) and the number of segmentations of the block (e.g., 4) may be set to preset values. The preset values may be set by input from a user.
[0058] In this case, the number of links (eg, 500) or the number of divisions (eg, 4) of the block set as a preset value is merely an exemplary value, and the present disclosure is not limited thereto.
[0059] Furthermore, in the repeated operation of the current geospatial embedding based on dynamic resolution, it is assumed that the entire country is first set to a block coordinate.
[0060] Thereafter, the processor 130 inserts the road link into the tree (S110). Generally speaking, road information consists of nodes and links. A node refers to a node of a road (eg, an intersection). A link refers to a route connecting these nodes.
[0061] For example, as described above, first, the link is inserted into a block that has been set up nationwide.
[0062] When the number of links inserted into the block is greater than the number of links that can be included in the block (Yes in S120), the processor 130 expands the tree by splitting the block (S130). That is, in the tree, when the number of links inserted into the block is greater than a preset value (ie, 500), the tree is expanded by splitting the block based on the number of splits of the block (eg, 4).
[0063] For example, it is understood that the expansion of a tree in which a block is divided into 4 includes internally decomposing a block including a number of links greater than a preset value into four small blocks.
[0064] For example, Figure 3 As shown, the tree can be extended by splitting a block into a fourth quadrant.
[0065] The processor 130 checks whether all the links have been inserted, and inserts all the links into the tree by repeating steps S110 to S130 (“No” in S140 ) until all the links are inserted into the tree.
[0066] When all the links are inserted into the tree (“Yes” in S140 ), the processor 130 assigns an ID to each block that has been finally divided ( S150 ).
[0067] That is, when the tree continues to expand and no longer expands and becomes a leaf node, data (ie, links) are divided at the leaf node.
[0068] In other words, this means that when a large block is internally broken down (reduced) into four small blocks and finally reduced to the smallest block, the data (ie, links) are divided in the smallest blocks.
[0069] Furthermore, the processor 130 assigns an ID to each block that has been finally segmented so that the ETA prediction model can use the corresponding geospatial information in the path search.
[0070] Reference Figure 3 ,It can be seen that, for each area, the blocks at locations where the links of the road network are congested (e.g., the city center area) are decomposed to the minimum (i.e., the number of links included in the blocks is reduced to 500 or less), while for each area, the blocks at locations where the links of the road network are not congested (e.g., in the suburbs of the city) have a relatively large size.
[0071] That is, the road network is generated in link units, and only one sheet of the road network with various types of resolutions is represented because the resolution of a road section with congested roads is deepened, while the resolution of a road section with uncongested roads is shallowed.
[0072] As reference Figure 4 As described above, static road network representation is a method of representing the entire area to be embedded at a specified resolution by continuously segmenting the entire area into latitudes and longitudes. In static road network representation, the entire road network can be represented at a desired resolution in a short time. However, the static road network representation has a problem in that if static segmentation is performed at a predetermined size, unnecessary data that does not include roads is generated, and multiple resolutions need to be used together to receive information related to the portion including the main road.
[0073] Figure 5 is an example diagram for describing an ETA prediction model of an apparatus for using a dynamic-resolution-based geospatial embedding search path according to an embodiment of the present disclosure.
[0074] The geospatial information based on the dynamic resolution (which has been represented as described above) can be used for ETA calculation by using it in the ETA prediction model described later.
[0075] Reference Figure 5 ,The structure of the ETA prediction model can be a linear model consisting of an embedding module and a transformer module.
[0076] In the embedding module, categorical data is embedded in d dimensions. Continuous data can be bucketized and then embedded in d dimensions. In this case, bucketization means converting continuous data into several features by dividing it into predetermined segments.
[0077] Time features, geospatial features, and situation features can be used as categorical data, and traffic information features and distance information features can be used as continuous data.
[0078] For example, an ETA prediction model according to an embodiment of the present disclosure (e.g., a deep learning model for ETA prediction) can use dynamic features including time information (e.g., which day of the week it is, which time zone of the day it is (e.g., 5-minute units), or which time zone of the week), geospatial features including ID information of blocks to which a dynamic block segmentation method has been applied (e.g., source ID, destination ID, and source ID-destination ID), traffic features including link speed information (e.g., real-time link speed or past link speed), contextual features including source and destination information, and distance features including length information of the path as input values.
[0079] In addition, each link type, each road type, link length, event (eg, accident or construction) information, link travel time of the routing search engine, and ETA information of the routing search engine may also be used as input values.
[0080] The transformer module can be composed of linear transformers and fully connected layers with smaller computational load than the ordinary transformer structure.
[0081] The ETA prediction model can learn the location information about where each link is located, and can learn the importance of the link according to the road conditions through the attention matrix. Different weights can be assigned between input features (i.e., higher weights are assigned to important features).
[0082] The i-th row of the LХL attention matrix of the linear transformer can be calculated as shown in Equation 1. In this case, the core function φ(․) is φ(x)=elu(x)+1=max(α(e x -1),0)+1. The attention value V' can be connected through residuals (such as f(X emb )=V'+X emb ) to be incorporated.
[0083] …… (1) The output value of the ETA prediction model can be the ETA values of all paths and / or the link passing times. That is, the ETA values of all paths can be directly predicted, or the passing times of each link in all paths can be predicted. In the latter case, the sum of the values of the link passing times can be used as the ETA prediction value.
[0084] However, the ETA prediction model according to an embodiment of the present disclosure can be implemented in various ways, in which the geospatial features using the above-described dynamic resolution embedding method are used as input values.
[0085] Figure 6 is a flowchart for describing a method of searching for a path using a geospatial embedding based on dynamic resolution according to an embodiment of the present disclosure. Figure 7 is a flowchart for describing the use of an ETA prediction model in a method of searching for a path using a geospatial embedding based on dynamic resolution according to an embodiment of the present disclosure.
[0086] As Figure 6 shown, the processor 130 receives a path search request (S200). For example, the processor 130 may receive a path search request from a user through an input module of a navigation device, including source information, destination information, and departure time information.
[0087] Thereafter, the processor 130 performs a path search using the ETA prediction model (S210).
[0088] Generally, such an operation for path search is based on a path search engine. The path search engine can search for a path from a source to a destination based on source information, destination information, and departure time information, and can select and output candidate paths suitable for various conditions (e.g., shortest distance, shortest time, and preference for free roads). However, the path search engine has been widely used in the technical field of the present disclosure, and thus further description thereof is omitted.
[0089] Therefore, as Figure 7 shown, the processor 130 selects a plurality of candidate paths based on the path search engine (S211). In this case, the selection of candidate paths based on the path search engine can be performed by calculating the cost of each link and calculating the candidate paths in the order of lower total cost. In this case, the cost of a link is a concept in which the cost for passing through the link has been digitized and can be calculated by considering the length of the link and the expected passing time of the link. In addition, the final cost of the corresponding path can be calculated by predicting the ETA of the candidate path and incorporating the predicted ETA into the cost.
[0090] However, the detailed method of calculating the cost of the search path may vary depending on the intention of the user, the design of the navigation system, etc.
[0091] In this case, the path search engine basically uses ETA to calculate candidate paths. In some embodiments, the path search engine may be configured to calculate candidate paths by including an ETA prediction model according to an embodiment of the present disclosure in the path search engine.
[0092] Alternatively, as will be described later, the path search engine selects candidate paths according to an existing method, but a method of recalculating costs by additionally performing ETA prediction using an ETA prediction model according to an embodiment of the present disclosure may also be used.
[0093] Therefore, the processor 130 calculates the ETA of the candidate path by using the ETA prediction model according to the embodiment of the present disclosure (S212). Next, the processor 130 calculates the cost of the candidate path based on the calculated ETA (S213).
[0094] Thereafter, the processor 130 derives a result of the path search based on the calculated cost (S214). That is, the processor 130 may calculate the cost again based on the calculated ETA of the candidate paths, and then may align the candidate paths in order of lower (or smaller) cost.
[0095] Next, the processor 130 provides a result of the route search (S220). That is, the processor 130 may provide a list of candidate routes and each ETA to the user as a result of the route search.
[0096] Although exemplary embodiments of the present disclosure are disclosed for illustrative purposes, it will be appreciated by those skilled in the art that various modifications, additions and substitutions may be made without departing from the scope and spirit of the present disclosure as defined in the appended claims. Therefore, the true technical scope of the present disclosure should be defined by the following claims.
Claims
1. A device for embedding a search path using geospatial information based on dynamic resolution, the device comprising: A storage module configured to store digital map data; as well as a processor configured to perform a route search based on an estimated arrival time prediction model in response to a route search request, Wherein, the estimated arrival time prediction model is based on a road network divided into multiple blocks.
2. The device according to claim 1, wherein: The estimated arrival time prediction model is based on the road network segmented into a plurality of blocks by a plurality of links merging into roads.
3. The device according to claim 2, wherein: The estimated arrival time prediction model is based on the road network divided into a plurality of blocks according to a maximum number of links that can be included in one block.
4. The device according to claim 3, wherein: The estimated arrival time prediction model is based on a tree expanded by inserting all links of the road network into the block and dividing the block into a preset number when the number of links inserted into one block is greater than the maximum number of links.
5. The device according to claim 4, wherein: The estimated arrival time prediction model is based on link information that is partitioned and stored in a leaf node when the tree becomes a leaf node that is no longer expanded.
6. The device according to claim 4, wherein: The estimated arrival time prediction model is based on identifier information assigned to each block that has been eventually partitioned into blocks where the tree is no longer extended.
7. The device according to claim 1, wherein: The estimated arrival time prediction model uses, as an input value, identifier information of the block including the link according to the path search.
8. The device according to claim 1, wherein: The processor calculates a plurality of candidate paths in response to the path search request, and calculates an estimated arrival time of each of the candidate paths by using the estimated arrival time prediction model.
9. The device according to claim 8, wherein: The processor calculates a cost of each of the candidate paths based on the calculated estimated arrival time of each of the candidate paths.
10. A method for generating an estimated arrival time prediction model, the method comprising: inserting, by a processor, road links of the road network into the tree; When the number of links inserted into a block of the tree is greater than the maximum number of links that can be included in one block, the processor expands the tree by dividing the block into a preset number; assigning, by the processor, identifier information to each block that has been eventually partitioned into blocks that are no longer to be extended by the tree; as well as The processor trains an estimated arrival time prediction model using identifier information of the block as an input value, the block including links of the path predicted according to the estimated arrival time.
11. The method according to claim 10, wherein: In the training of the estimated arrival time prediction model, the processor trains the estimated arrival time prediction model by further using a dynamic feature including time information and a traffic feature including passing speed information of the link as the input values.
12. The method according to claim 10, wherein: The estimated arrival time prediction model outputs the link transit time as an output value.
13. The method according to claim 10, wherein: The estimated arrival time prediction model outputs the estimated arrival time of all paths as output values.
14. A method for embedding a search path using geospatial information based on dynamic resolution, the method comprising: Receiving, by the processor, a path search request; performing, by the processor, a path search based on an estimated arrival time prediction model; as well as The processor provides the result of the path search, Wherein, the estimated arrival time prediction model is based on a road network divided into multiple blocks.
15. The method according to claim 14, wherein: Executing the path search includes: calculating, by the processor, a plurality of candidate paths in response to the path search request; and The processor calculates the estimated arrival time of each of the candidate paths using the estimated arrival time prediction model.
16. The method according to claim 15, wherein: Performing the path search further includes calculating, by the processor, a cost of each of the candidate paths based on the calculated estimated arrival time of each of the candidate paths.
17. The method according to claim 14, further comprising training, by the processor, the estimated arrival time prediction model by using identifier information of the block as an input value before receiving the path search request, the block including links of the path predicted according to the estimated arrival time.
18. The method according to claim 17, wherein: The estimated arrival time prediction model is based on the road network divided into the plurality of blocks according to a maximum number of links that can be included in one block.
19. The method according to claim 18, wherein: The estimated arrival time prediction model is based on a tree expanded by inserting all links of the road network into the block and dividing the block into a preset number when the number of links inserted into one block is greater than the maximum number of links.
20. The method according to claim 19, wherein: The estimated arrival time prediction model is based on link information that is partitioned and stored in a leaf node when the tree becomes a leaf node that is no longer expanded.