WO2019024344A1 - 基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法 - Google Patents

基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法 Download PDF

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WO2019024344A1
WO2019024344A1 PCT/CN2017/113471 CN2017113471W WO2019024344A1 WO 2019024344 A1 WO2019024344 A1 WO 2019024344A1 CN 2017113471 W CN2017113471 W CN 2017113471W WO 2019024344 A1 WO2019024344 A1 WO 2019024344A1
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query
trajectory
correlation
spatial
source
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French (fr)
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毛睿
李荣华
陆敏华
王毅
罗秋明
商烁
刘刚
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深圳大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/95—Retrieval from the web
    • G06F16/953—Querying, e.g. by the use of web search engines
    • G06F16/9535—Search customisation based on user profiles and personalisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/95—Retrieval from the web
    • G06F16/953—Querying, e.g. by the use of web search engines
    • G06F16/9537—Spatial or temporal dependent retrieval, e.g. spatiotemporal queries

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  • the invention belongs to a location-based service in the field of computer spatial data, and in particular relates to a heuristic expansion search expansion algorithm based on a track query with a sequenced interest region.
  • trajectory search queries are generally classified into three categories.
  • the query parameter is a single spatial point, and the query looks for a trajectory that is spatially close to the query point.
  • Zheng et al. [K. Zheng, B. Zheng, J. Xu, G. Liu, A. Liu, and Z. Li. Popularityaware spatial keyword search on activity trajectories. World Wide Web, 19(6): 1–25, Online first, 2016.] Extend this query to the overlay space and text field, and propose a TkSK query to retrieve the trajectory spatially close to the query point to meet the semantic requirements of the query definition.
  • the query requires a set of locations (such as a sightseeing place) as parameters to return a link or a trajectory that approximates the query location according to some criteria.
  • locations such as a sightseeing place
  • TTL location-based trajectory search
  • the query parameters are a set or series of locations.
  • a place may not be the location of a point, but it may be a region of interest that contains several spatial objects.
  • the user may not be able to accurately specify the intended location, instead using the intended area instead.
  • TSR trajectory search interest
  • the present invention investigates a trajectory search interest (TSR) query by region, which aims to find a trajectory that has the highest correlation with the spatial density of the query region.
  • TSR queries are not valid for TSR queries for two reasons. First, TSL only considers space, while TSR takes into account spatial distance and spatial object density. Second, TSL is only performed in Euclidean space, and spatial index (for example, R-tree [A. Guttman. R-trees: a dynamic index structure for spatial searching. In SIGMOD, pages 47-57, 1984.]) is used. Improve query efficiency. But in our work, movement is limited to the space network.
  • the lower bound distance of the network may not be the corresponding Euclidean distance; therefore, spatial indicators such as R-tree are invalid of. This is the main reason we use network extensions (ie, Dijkstra's extension).
  • TSR query and its solution are different from PNC query.
  • the solution has the following six aspects: (i) query type: PNC query is spatial density query on space and density domain, and TSR query is spatial query (density also It is considered, but the query processing only occurs in the spatial domain).
  • Query parameters and results The PNC query takes the route as a parameter and returns a top-k cluster with the highest distance-density for the query route, while the TSR query takes a set of regions of interest as parameters and returns the highest spatial density. Off track.
  • Similarity function The similarity function is used for PNC queries to calculate the correlation of distance and density in the spatial and density domain, and their linear combination. In the spatial domain, it measures the network distance between the cluster center and the route; and in the density domain, calculates the density of the cluster.
  • the similarity function of the TSR query evaluates the spatial density correlation between the trajectory and a set of query regions. The distance between the trajectory and all spatial objects in the query area is taken into account.
  • the technical problem to be solved by the present invention is to provide a heuristic expansion search expansion algorithm based on a trajectory query with a sequenced region of interest, given a trajectory parameter set, and a TSR query requires a set of regions of interest as a parameter, and Returns the track with the highest spatial density associated with the query area in the track set.
  • This type of query can be used for many popular applications, such as trip planning and recommendations, and location-based services, extending the scope of applications.
  • the invention solves the problem that the existing TSL solution is invalid for TSR query (track-based query based on region of interest), and the existing PNC solution is not applicable to the TSR problem.
  • the algorithm further reduces the search space, avoids traversal of overlapping regions, and further improves query performance.
  • the extended algorithm can effectively process TSR queries with sequences.
  • the present invention develops a heuristic expansion search extension algorithm (BES) based on a tracked query of a sequenced region of interest.
  • BES heuristic expansion search extension algorithm
  • the algorithm has the following advantages: (1) further reducing the search space and avoiding traversal of overlapping regions; (2) effective heuristic search strategies focus on those trajectories that are easier to solve, further improving query performance; Effectively process TSR queries with sequences.
  • a heuristic expansion search expansion algorithm based on a tracked query with a sequenced region of interest includes the following steps:
  • C' sd (c, v) is the spatial density correlation between the query regions c and v
  • C' sd (C, v) represents the space of the query region set C and the trajectory ⁇ Density correlation
  • p i . g is the number of spatial objects attached to p i
  • sd(p,v) represents the distance between point p and point v
  • *.head represents the first element in the list
  • *.tail indicates the list except for head a list of all the elements
  • Step 2 Select a group of query sources from the query area center
  • Step 3 All query source priorities are initially set to 0; heuristic search is performed according to the priority ranking from each query source;
  • Step 4 Calculate the upper and lower limits of the spatial density, update LB and UB;
  • Step 6 Sort the trajectory according to the value of the upper limit of the spatial density
  • Step 7 Further refinement according to the trajectory ordering, returning the trajectory with the largest spatial density correlation.
  • a query source selection policy is used to select a set of query sources from the query region center, and the query source selection strategy is: given a set of spatial objects O and query traces q, if the query Source c has a high spatial object density and is spatially close to q, returning query source c.
  • the heuristic search according to the priority ranking from each query source is specifically: using a heuristic scheduling strategy based on priority ranking to perform Dijkstra expansion algorithm, each query source Pn has a label pl describing its priority, maintaining a dynamic priority heap on the pl containing these query sources, and defining the priority of each query source pl as follows:
  • T p is a set of partial coverage trajectories
  • T s (p) is a set of trajectories covered by a search range starting from p
  • C' sd (C, ⁇ ) is a spatial density correlation of the trajectory ⁇ and the set of query regions C, C ' sd (C, ⁇ ).ub represents the upper limit of this correlation.
  • the upper and lower limits of the calculated spatial density are specifically: for each newly scanned trajectory, if it is not scanned by the extended scan starting from p, it is marked as having been scanned by p , calculate its upper limit of spatial density C' sd (C, ⁇ ).ub and the lower limit C' sd (C, ⁇ ). lb;
  • the lower bound of space density is estimated as:
  • the upper limit of the spatial density is estimated as:
  • C is the set of query regions
  • ⁇ is a trajectory
  • C' sd (C, ⁇ ) is the spatial density dependence of the trajectory ⁇ and the set of query regions C, C' sd (C, ⁇ ).
  • lb represents this correlation
  • C.head represents the first query region in set C
  • ⁇ .head represents the first element in ⁇
  • lb represents the lower bound of the correlation between C.head and ⁇ .head in the query area
  • C' sd (C.head, ⁇ .head).ub represents the upper limit of the correlation between C.head and ⁇ .head in the query area.
  • C.tail represents a list of all query areas except C.head in the list.
  • C' sd (C.tail, ⁇ ) represents the correlation between the query region set C.tail and the track ⁇
  • C' sd (C , ⁇ .tail) represents the correlation of the query region set C with the trajectory ⁇ .tail;
  • the new query region and the upper and lower bounds of the track space density are estimated by taking c2, ⁇ 1 as an example:
  • p1 is a query source
  • p2 is the center of the query area c 2
  • p1 is the nearest query source from p2
  • ⁇ 1 is a track.
  • p i. g is the number of spatial objects attached to p i
  • d M (p1, ⁇ 1) represents the network distance between point p1 and trajectory ⁇ 1
  • sd(p i , p 2 ) represents point p i and point p 2 The distance between the networks.
  • C 1 indicates that ⁇ is covered by the search range from the center of c 1
  • C 2 indicates that ⁇ is not covered by the search range from the center of c 1
  • Re i represents the radius of the search range from the center of c i .
  • the update LB and UB in step 4 are specifically: if C' sd (C, ⁇ ). lb > LB, the LB is updated to C' sd (C, ⁇ ). lb; if C ' sd (C, ⁇ ).ub ⁇ UB, UB updated to C' sd (C, ⁇ ).ub.
  • the neighboring query source extension of the network in step 5 is terminated, the trajectory with the upper limit of the spatial density less than LB is deleted from Tf , and Tf is the set of all the completely covered trajectories; if p is not The highest ranked query source, the network terminated from the extension of p, began to search for the new ranking first query source.
  • the trajectories in T f in step 6 are sorted according to the value of the upper limit of the spatial density.
  • the present invention has the following beneficial effects:
  • the present invention is based on the region of interest; the present invention solves the problem that the existing TSL solution is invalid for the TSR query, and the existing PNC solution is not applicable to the TSR problem.
  • the present invention further reduces the search space and avoids traversal of overlapping regions; the effective heuristic search strategy of the present invention focuses on those trajectories that are easier to be solutions, and further improves query performance.
  • the traveler can specify a sequence for accessing the intended area (eg, C1, C2, and C3 are predetermined areas, the order of access is C1 ⁇ C2 ⁇ C3), and the user can specify a sequence of preferred access to the query area. In this situation, the order of each region needs to be considered.
  • the algorithm of the present invention solves the above technical problems by considering the order of each region, and can effectively process the TSR query with sequence.
  • FIG. 1 is a flow chart of a heuristic expansion search expansion algorithm based on a tracked query of a sequenced region of interest according to the present invention.
  • FIG. 2 is a schematic diagram of an example of a TSR query of the present invention.
  • Figure 3 is a schematic illustration of an embodiment of spatial density correlation of the present invention.
  • FIG. 4 is a schematic diagram of an example of a heuristic expansion search expansion algorithm (BES algorithm) based on a trajectory query with a sequenced region of interest according to the present invention.
  • BES algorithm heuristic expansion search expansion algorithm
  • FIG. 5 is a schematic diagram showing the influence of different trajectory numbers on experimental results according to the present invention. wherein FIG. 5(a) represents the influence of different trajectories on the running time in Beijing Road Network (BRN); FIG. 5(b) represents Beijing Road Network ( Number of access trajectories in different trajectories in BRN).
  • BRN Beijing Road Network
  • the system of the invention is defined as follows:
  • V is the set of vertices
  • I a set of edges.
  • the vertex vi ⁇ V represents the road intersection or end point.
  • the function F: V ⁇ E ⁇ Geometries records the geometric information of the spatial network. In particular, it maps the vertices and edges to the points of the respective road intersections and the polylines representing the corresponding road segments.
  • W:E ⁇ R assigns weights to each edge.
  • the weight of the edge e, W(e) represents the length of the corresponding link or some other relevant property such as fuel consumption or travel time, which can be obtained by mining historical traffic data.
  • vi (pi, ti)
  • the area of interest is a subgraph Contains vertex cV and edge cE, defined by center vm and radius r, where c.vm is the vertex in G: r is the network distance from c to the area boundary.
  • the spatial influence factor I(p1, p2) is defined as follows:
  • ⁇ is a threshold.
  • the value of I(p1, p2) is inversely proportional to sd(p1, p2). If the distance between p1 and p2 reaches the threshold, the influence factor between them is set to zero.
  • the threshold is used to further trim the trajectory from the query area.
  • the value of I(p1, p2) is in the range [0, e - ⁇ ], e - ⁇ ⁇ (0, 1).
  • pi is a vertex belonging to c
  • p ⁇ is the vertex closest to the center c.m of the region.
  • Pi.g is the number of spatial objects connected to pi. Both spatial distance and spatial object density are taken into account. These functions extend the well-known longest common subsequence (LCSS) by considering the density of spatial objects.
  • LCSS longest common subsequence
  • each region plays an equally important role, so we use the Sigmoid function to normalize the spatial density correlation C sd (c, ⁇ ) to the range [0, 1].
  • the Sigmoid function is as follows:
  • C'sd(c, v) is the spatial density correlation between the query areas c and v.
  • C'sd(C,v) represents the spatial density correlation of the set of query regions C with the trajectory ⁇ .
  • Pi.g is the number of spatial objects attached to pi.
  • Sd(p,v) represents the distance between point p and point v.
  • *.head represents the first element in the list, and *.tail represents a list of all elements except the head in the list.
  • BES algorithm heuristic expansion search extension algorithm
  • the algorithm has two major advantages: (1) further reducing the search space and avoiding traversal of overlapping regions; (2) effective heuristic search strategies focus on those trajectories that are easier to solve, further improving query performance; Can effectively process TSR queries with sequences.
  • the specific steps of the algorithm of the present invention are as follows:
  • the global spatial density correlation lower limit LB is set to 0, and the global spatial density correlation upper limit UB is set to + ⁇ .
  • An existing query source selection strategy refers to: given a set of spatial objects O (eg, POI, geotagged photos or geotagged tweets) and query track q, if query source c has a high spatial object density and is in space When the top is close to q, the query source c is returned.
  • O eg, POI, geotagged photos or geotagged tweets
  • T p is a set of partial coverage trajectories
  • T s (p) is a set of trajectories covered by a search range starting from p
  • C' sd (C, ⁇ ) is a spatial density correlation of the trajectory ⁇ and the set of query regions C, C ' sd (C, ⁇ ).ub represents the upper limit of this correlation.
  • the priority tag of all query sources is set to 0, and at each step, we search for the highest ranked query source (a maximum priority tag) and perform network expansion according to Dijkstra's algorithm. For each newly scanned track, if it is not scanned for an extended scan starting from p, it is marked as having been scanned by p.
  • the BES algorithm further reduces the search space, thereby avoiding traversal of overlapping regions.
  • the upper and lower bounds of the spatial density correlation between the query region set C and the trajectory ⁇ are:
  • the lower bound of space density is estimated as:
  • the upper limit of the spatial density is estimated as:
  • C is the set of query regions
  • ⁇ is a trajectory
  • C' sd (C, ⁇ ) is the spatial density dependence of the trajectory ⁇ and the set of query regions C, C' sd (C, ⁇ ).
  • lb represents this correlation
  • C.head represents the first query region in set C
  • ⁇ .head represents the first element in ⁇
  • lb represents the lower bound of the correlation between C.head and ⁇ .head in the query area
  • C' sd (C.head, ⁇ .head).ub represents the upper limit of the correlation between C.head and ⁇ .head in the query area.
  • C.tail represents a list of all query areas except C.head in the list.
  • C' sd (C.tail, ⁇ ) represents the correlation between the query region set C.tail and the track ⁇
  • C' sd (C , ⁇ .tail) represents the correlation of the query region set C with the trajectory ⁇ .tail;
  • BES defines the new query region and the upper and lower bounds of the trajectory space density estimation formula (taking c2, ⁇ 1 as an example):
  • p1 is a query source
  • p2 is the center of the query area c 2
  • p1 is the nearest query source from p2
  • ⁇ 1 is a track.
  • p i. g is the number of spatial objects attached to p i
  • d M (p1, ⁇ 1) represents the network distance between point p1 and trajectory ⁇ 1
  • sd(p i , p 2 ) represents point p i and point p 2 The distance between the networks.
  • C 1 indicates that ⁇ is covered by the search range from the center of c 1
  • C 2 indicates that ⁇ is not covered by the search range from the center of c 1
  • Re i represents the radius of the search range from the center of c i .
  • the trajectory is sorted in Tf from the largest to the smallest according to the value of C sd (C, ⁇ ).ub.
  • C sd C, ⁇ ).ub.
  • ⁇ p1, p2, ..., pi ⁇ is the vertex closest to the center of the region ⁇ c1.m, c2.m, ..., ci.m ⁇ .
  • Tr is a set of refined trajectories
  • the refinement is terminated, and all unrefined trajectories are Pruning. Returns the track with the highest spatial density correlation.
  • FIG. 2 shows an example of a TSR query.
  • c1, c2, and c3 are TSR query areas
  • p1, p2, and p3 are the corresponding area centers
  • r1, r2, and r3 are radii.
  • Points p3, p4, ..., p8 are the sampling points within the track.
  • ⁇ 1, p6, p7, and p8 are sampling points closest to the centers p1, p2, and p3, respectively.
  • p4 and p5 are the sampling points closest to the centers p1 and p2, respectively.
  • Each region contains several spatial objects.
  • the trajectory ⁇ 2 is returned only when spatial proximity to the center of the region is taken into account because the trajectory ⁇ 2 is spatially closest to the center of the region. If we consider the distribution of spatial objects, the trajectory ⁇ 2 is less attractive than the trajectory ⁇ 1 because it is farther away from the region where the spatial object density is high.
  • the trajectory ⁇ 1 is the best choice when considering both of the above aspects (although the trajectory ⁇ 2 is slightly better in spatial distance than ⁇ 1).
  • Figure 3 shows an embodiment of spatial density correlation.
  • ⁇ is a trajectory
  • c1 and c2 are two regions
  • p1 and p2 are their centers, respectively.
  • the vertices ⁇ p3, p4 ⁇ ⁇ are the points closest to p1 and p2 on ⁇ , ⁇ p5, p6, p7, p8 ⁇ ⁇ c1, ⁇ p9, p10 ⁇ ⁇ c2.
  • SP(p2, p1) + SP(p1, p5) is a path from p2 to ⁇ 1, and thus dM(pm, ⁇ ) ⁇ dM(pn, ⁇ ) + sd(pm, pn) is obtained.
  • the track set size in the BRN is set to 600,000, and when the NRN is set to 1000,000, the track length is set to 20 in the BRN, set to 100 in the NRN, and the number of query areas in the BRN and BRN is set to 6.
  • the average radius of the query area varies from 2 km to 10 km, at BRN (default 6 km); at NRN (default 150 km) varies from 50 km to 250 km.
  • BES Pruning rate (BRN) 0.76 Reservation rate (BRN) 0.24 Pruning rate (NRN) 0.69 Reservation rate (NRN) 0.31
  • Figure 5 shows the performance of the algorithm for the number of different trajectories
  • causes more trajectories to be processed and produces a larger trajectory search space. Therefore, both the CPU time and the number of access trajectories under the algorithm of the present invention will be higher.

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Abstract

本发明公开了一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法，包括如下步骤：1：初始设置全局空间密度相关性下限LB＝0，全局空间密度相关性上限UB＝+∞；2：从查询区域中心中选择一组查询源；3：所有查询源优先级初始设置为0；从每个查询源按照基于优先级排名进行启发式搜索；4：计算空间密度的上限和下限，更新LB和UB；5：判断LB>UB或所有搜索半径超过ε+p.dist/2是否成立，如成立则进入下一步；如不成立则回到上一步；6：根据空间密度上限的值对轨迹进行排序；7：按照轨迹排序细化，返回具有最大空间密度相关性的轨迹。本发明解决了传统轨迹搜索对TSR查询无效的问题，减小搜索空间，避免重叠区域的遍历，提高查询性能，有效处理带序列的TSR查询。

Description

基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法 技术领域
本发明属于计算机空间数据领域基于位置的服务，尤其涉及一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法。
背景技术
一般将现有的轨迹搜索查询分为三类。在点对点轨迹查询类别中，查询参数是单个空间点，并且查询寻找空间上靠近查询点的轨迹。郑等人[K.Zheng,B.Zheng,J.Xu,G.Liu,A.Liu,and Z.Li.Popularityaware spatial keyword search on activity trajectories.World Wide Web,19(6):1–25,online first,2016.]将此查询扩展到覆盖空间和文本域，并提出TkSK查询来检索在空间上靠近查询点的轨迹，以满足查询定义的语义要求。在点到轨迹查询类别中，查询需要一组地点(如观光场所)作为参数，返回一条连接或根据某种标准接近查询位置的轨迹。基于位置的轨迹搜索的概念(TSL)首先由Chen等提出[Z.Chen,H.T.Shen,X.Zhou,Y.Zheng,and X.Xie.Searching trajectories by locations:an efficiency study.In SIGMOD,pages 255–266,2010.]。这个研究仅考虑空间域(欧几里德空间)。尚等[S.Shang,R.Ding,B.Yuan,K.Xie,K.Zheng,and P.Kalnis.User oriented trajectory search for trip recommendation.In EDBT,pages156–167,2012.]观察到由于用户的特定偏好，空间相似性没有充分捕捉查询位置与轨迹之间的关系。然后他们提出以用户为导向的轨迹搜索并扩展查询覆盖空间和文本域。直观地，如果轨迹接近指定的查询位置(空间域)，其文本属性值与用户的文字偏好(文字域)类似，将会被推荐给用户。在轨迹到轨迹类别中，查询检索与查询轨迹最相似的轨迹。例如，PTM查询[S.Shang,R.Ding,K.Zheng,C.S.Jensen,P.Kalnis,and X.Zhou.Personalized trajectory matching in spatial networks.VLDB J.,23(3):449–468,2014.]考虑时空相似性，ATSQ查询[K.Zheng,S.Shang,N.J.Yuan,and Y.Yang.Towards efficient search for activity trajectories.In ICDE,pages 230–241,2013.]考虑空间-文本相似性。
在大多数现有的研究轨迹搜索中，查询参数是一组或一系列的位置。然而，在某些情况下，一个地方可能不是一个点的位置，但可能是包含几个空间对象的感兴趣区域。此外，特别是当规划一个在陌生城市的旅行时，用户可能无法准确指定预期地点，而使用预期区域代替。这两个常见的案例正是现有轨迹搜索方法存在的问题或缺陷。
与现有研究不同，本发明研究按地区进行轨迹搜索的兴趣(TSR)查询，它旨在找到一个与查询区域的空间密度相关性最高的轨迹。现有的TSL解决方案对TSR查询无效，有两个原因。首先，TSL只考虑空间，而TSR考虑到空间距离和空间物体密度。二是TSL只在欧氏空间中进行，空间索引(例如，R-tree[A.Guttman.R-trees:a dynamic index structure for spatial searching.In SIGMOD,pages 47–57,1984.])用于提高查询效率。但在我们的工作中，运动被限制到空间网络。当网络中的边的权重是对旅行的许多方面(例如，燃料消耗和旅行时间)建模，网络的下限距离可能不是相应的欧几里德距离；因此，诸如R-tree等空间指标是无效的。这是我们使用网络扩展的主要原因(即，Dijkstra的扩展)。
最相关的工作可以说是集群附近的路径(PNC)查询[S.Shang,K.Zheng,C.S.Jensen,B.Yang,P.Kalnis,G.Li,and J.Wen.Discovery of path nearby clusters in spatial networks.IEEE Trans.Knowl.Data Eng.,27(6):1505–1518,2015.]，因此我们在此详细介绍。TSR查询及其解决方案与PNC查询不同，其解决方案有以下六个方面：(i)查询类型：PNC查询是在空间和密度域上进行的空间密度查询，而TSR查询是空间查询(密度也被考虑，但查询处理仅发生在空间域)。(ii)查询参数和结果：PNC查询以路由为参数，并返回关于查询路由具有最高距离-密度的top-k簇，而TSR查询将一组感兴趣的地区作为参数并返回具有最高空间密度相 关的轨迹。(iii)相似度函数：相似度函数用于PNC查询，会计算距离和密度在空间和密度领域的相关性，以及它们的线性组合。在空间域中，它测量集群中心与路由之间的网络距离；并且在密度域中，计算簇的密度。TSR查询的相似度函数评估轨迹与一组查询区域之间的空间密度相关性。轨迹和查询区域内所有空间对象之间的距离均被考虑在内。(iv)数据模型和算法结构：对于PNC查询，集群的密度映射到一维空间(密度域)，PNC查询处理搜索此域以查找高空间物体密度的集群。TSR查询没有单独的密度域。空间物体的密度是轨迹与查询区域中空间物体之间的距离的总和。由于这些差异，PNC和TSR要求不同的算法。(v)优化技术：由于以上与PNC的差异，TSR需要具体优化技术。因TSR查询具有多个查询区域参数，需要一个策略来安排多个查询区域。TSR重用并扩展查询源选择PNC方法(方程式12-14)来从查询区域中选择查询源。(vi)实验空间数据集：使用不同的空间数据集。对于PNC查询，空间对象是地理标记的微博帖子，轨迹数据没有使用，而对于TSR查询，空间对象是使用兴趣点和真实或合成的轨迹数据。由于这六个差异，TSR查询及其解决方案是新的。PNC解决方案不适用于TSR问题。
发明内容
本发明要解决的技术问题在于提供一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法，其给定一个轨迹参数集合，一个TSR查询需要一组感兴趣的区域作为一个参数，并返回在轨迹集中与查询区域的空间密度相关性最高的轨迹。这种类型的查询可用于许多流行的应用，如行程规划和建议，和基于位置的服务，扩展了应用范围。本发明解决了现有的TSL解决方案对TSR查询(基于兴趣区域的轨迹查询)无效，现有的PNC解决方案不适用于TSR问题。该算法进一步减小了搜索空间，避免重叠区域的遍历，且进一步提高查询性能。此外，该扩展算法能有效处理带序列的TSR查询。
本发明开发一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法(BES)。首先，我们利用现有的查询源选择策略(参见S.Shang,K.Zheng,C.S.Jensen,B.Yang,P.Kalnis,G.Li,and J.Wen.Discovery of path nearby clusters in spatial networks.IEEE Trans.Knowl.Data Eng.,27(6):1505–1518,2015.)从查询区域的中心选择一组查询源。其次，我们定义新的空间密度上界和下界来剪枝搜索空间。第三、基于优先级排名的启发式搜索战略调度使用多个查询源。我们保持和使用处理查询时的动态优先级排序堆。在每一个时间点，我们扩展排名最高的查询源，直到一个新的查询源成为顶级。该算法有以下优势：(一)进一步减小了搜索空间，避免重叠区域的遍历；(二)有效启发式搜索策略侧重于那些更容易是解决方案的轨迹，进一步提高查询性能；(三)能有效处理带序列的TSR查询。
为解决上述技术问题，一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法，包括如下步骤：
步骤1：初始设置全局空间密度相关性下限LB＝0，全局空间密度相关性上限UB＝+∞；定义空间密度相关性计算公式：
Figure PCTCN2017113471-appb-000001
Figure PCTCN2017113471-appb-000002
其中，v是轨迹τ上的点，C’sd(c,v)是查询区域c与v之间的空间密度相关性；C’sd(C,v)表示查询区域集合C与轨迹τ的空间密度相关性；pi。g是附属于pi的空间对象的数量；sd(p,v) 代表点p与点v之间的距离；*.head表示列表中第一个元素，*.tail表示列表中除head之外的所有元素构成的列表；
步骤2：从查询区域中心中选择一组查询源；
步骤3：所有查询源优先级初始设置为0；从每个查询源按照基于优先级排名进行启发式搜索；
步骤4：计算空间密度的上限和下限，更新LB和UB；
步骤5：判断LB>UB或所有搜索半径超过ε+p.dist/2是否成立，其中，ε是事先设置的阈值，p.dist＝max{sd(p,p’),sd(p,p”)}，p’和p”是p的邻近查询源，sd(p,p’)代表点p和点p’之间的网络距离，sd(p,p”)代表点p和点p”之间的网络距离；如成立则网络的相邻查询源扩展终止，进入下一步骤6；如不成立，则回到步骤4；
步骤6：根据空间密度上限的值对轨迹进行排序；
步骤7：按照轨迹排序进一步细化，返回具有最大空间密度相关性的轨迹。
作为本发明优选的技术方案，步骤2中，利用查询源选择策略从查询区域中心中选择一组查询源，所述查询源选择策略为：给定一组空间对象O和查询轨迹q，如果查询源c具有高的空间对象密度并且在空间上接近于q，则返回查询源c。
作为本发明优选的技术方案，步骤3中，所述从每个查询源按照基于优先级排名进行启发式搜索具体为：采用基于优先级排名的启发式调度策略进行Dijkstra扩展算法，每个查询源pn都有一个标签p.l描述它的优先级，在包含这些查询源的p.l上维护一个动态的优先级堆，定义每个查询源p.l的优先级如下:
Figure PCTCN2017113471-appb-000003
其中，p.c是一个包含了查询源p和所有以p为最近查询源的非查询源的查询区域中心的集合，|p.c|是它的大小。Tp是部分覆盖轨迹的集合，Ts(p)是被从p开始的搜索范围覆盖的轨迹集合；C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).ub代表这个相关性的上限。
作为本发明优选的技术方案，步骤4中，所述计算空间密度的上限和下限具体为：对于每一个新扫描的轨迹，如果没有被从p开始的扩展扫描，它被标记为已被p扫描，计算其空间密度上限C’sd(C,τ).ub和下限C’sd(C,τ).lb；
对于查询源，空间密度下限估算公式为：
Figure PCTCN2017113471-appb-000004
对于查询源，空间密度上限估算公式为：
Figure PCTCN2017113471-appb-000005
其中，C是查询区域集合，τ是一条轨迹，C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).lb代表这个相关性的下限，C’sd(C,τ).ub代表这个相关性的上限；C.head 表示集合C中第一个查询区域，τ.head表示τ中第一个元素，C’sd(C.head,τ.head).lb表示查询区域C.head与τ.head相关性的下限，C’sd(C.head,τ.head).ub表示查询区域C.head与τ.head相关性的上限，C.tail表示列表中除C.head之外的所有查询区域构成的列表，C’sd(C.tail,τ)代表查询区域集合C.tail与轨迹τ的相关性，C’sd(C,τ.tail)代表查询区域集合C与轨迹τ.tail的相关性；
对于非查询源的查询区域中心，新的查询区域与轨迹空间密度上下界估算公式为，以c2，τ1为例：
Figure PCTCN2017113471-appb-000006
其中，p1是一个查询源，p2是查询区域c2的中心，是一个非查询源，p1是离p2最近的查询源，τ1是一条轨迹。pi.g是附属于pi的空间对象的数量，dM(p1,τ1)代表点p1与轨迹τ1之间的网络距离，sd(pi,p2)代表点pi和点p2之间的网络距离。
Figure PCTCN2017113471-appb-000007
其中，C1表示τ被从c1的中心开始的搜索范围覆盖，C2表示τ没有被从c1的中心开始的搜索范围覆盖。rei表示从ci的中心开始的搜索范围的半径。
作为本发明优选的技术方案，步骤4中所述更新LB和UB具体为：如果C’sd(C,τ).lb>LB，LB更新为C’sd(C,τ).lb；如果C’sd(C,τ).ub<UB，UB更新为C’sd(C,τ).ub。
作为本发明优选的技术方案，步骤5中所述网络的相邻查询源扩展终止，空间密度上限小于LB的轨迹从Tf中删除，Tf是所有被完全覆盖的轨迹的集合；如果p不是排名最高的查询源，网络中从p的扩展终止，开始搜索新排名第一的查询源。
作为本发明优选的技术方案，步骤6中Tf中的轨迹根据空间密度上限的值排序。
作为本发明优选的技术方案，步骤7中所述按照轨迹排序进一步细化，具体为：对于轨迹τ∈Tf，假设{p1,p2,...,pi}是最靠近区域中心{c1.m,c2.m,...,ci.m}的顶点，从{p1,p2,...,pi}执行Dijkstra扩展算法来计算pi和区域ci内顶点之间的网络距离，一旦
Figure PCTCN2017113471-appb-000008
所述细化终止，返回具有最大空间密度相关性的轨迹；其中Tr是已经被细化的轨迹集合，Tu是未被细化的轨迹集合，Tr∪Tu＝Tf，τ’是Tu中的一条轨迹。
与现有技术相比，本发明具有以下有益效果：
1、与传统轨迹搜索(TSL)查询不同，本发明是基于兴趣区域的；本发明解决了现有的TSL解决方案对TSR查询无效，现有的PNC解决方案不适用于TSR问题。
2、本发明进一步减小了搜索空间，避免重叠区域的遍历；本发明有效启发式搜索策略侧重于那些更容易是解决方案的轨迹，进一步提高查询性能。
3、在某些情况下，旅行者也有可能指定访问预期区域的序列(例如，C1，C2和C3是预定区域，访问顺序为C1→C2→C3)，用户可以指定首选访问查询区域的序列。在这种情 况下，需要考虑到各区域的顺序。本发明算法就考虑到各区域的顺序，解决了上述技术问题，能有效处理带序列的TSR查询。
4、经实验验证，一个更大的轨迹数导致更多的轨迹被处理并产生更大的轨迹搜索空间，采用本发明算法，CPU时间和访问轨迹数都将更高。
附图说明
下面结合附图和实施例对本发明进一步说明。
图1是本发明基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法的流程图。
图2是本发明TSR查询实例示意图。
图3是本发明空间密度相关性的实施例示意图。
图4为本发明基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法(BES算法)的一个实例示意图。
图5为本发明的不同轨迹数对实验结果的影响示意图；其中，图5(a)代表北京路网(BRN)中不同轨迹数量对于运行时间的影响；图5(b)代表北京路网(BRN)中不同轨迹数量下的访问轨迹数。
具体实施方式
现在结合附图对本发明作进一步详细的说明。这些附图均为简化的示意图，仅以示意方式说明本发明的基本结构，因此其仅显示与本发明有关的构成。
本发明系统定义如下：
空间网络
我们将空间网络建模为一个无向连通图G(V,E,F,W)，其中V是顶点集，
Figure PCTCN2017113471-appb-000009
是一个边集。顶点vi∈V表示道路交叉点或终点。定义边ek＝(vi，vj)∈E通过两个顶点，并表示路段顶点vi和vj之间的行进功能。函数F：V∪E→Geometries记录空间网络的几何信息.特别地，它将顶点和边分别映射到相应道路交叉口的点和代表相应路段的折线。函数W：E→R给每个边分配权重。边e的权重W(e)代表相应的路段长度或一些其他相关性质如燃油消耗或旅行时间，可以通过挖掘历史交通数据获得。
轨迹
轨迹是一个有限的有序序列<v1,v2,...,vn>，其中vi＝(pi,ti)，其中pi是样点(在顶点处)，ti是时间戳。在这项研究中，我们只考虑轨迹的空间属性。
兴趣区域
兴趣区域是一个子图
Figure PCTCN2017113471-appb-000010
包含顶点c.V和边c.E，通过中心vm和半径r定义，其中c.vm是G中的顶点：r是从c到区域边界的网络距离。
空间密度相关性
给定空间网络中的任何两个顶点pa和pb，它们之间的网络最短路径由SP(pa，pb)表示，其长度由sd(pa,pb)表示。给出一个轨迹τ和空间网络中的顶点o，最小距离顶点o和轨迹τ之间的dM(o,τ)定义为：
Figure PCTCN2017113471-appb-000011
其中pi是τ中的点。
给定两个空间点p1和p2，空间影响因子I(p1,p2)定义如下：
Figure PCTCN2017113471-appb-000012
ε是一个阈值。I(p1,p2)的值与sd(p1，p2)成反比。如果p1和p2之间的距离达到阈值，则设置它们之间的影响因子是0。阈值用于从查询区域进一步修剪轨迹。I(p1,p2)的值在范围内[0，e-ε]，e-ε∈(0，1)。
一个区域c与轨迹τ之间的空间密度相关性Csd(c,τ)定义如下：
Figure PCTCN2017113471-appb-000013
这里，pi是属于c的顶点，p∈τ是最接近区域中心c.m的顶点。pi.g是连接到pi的空间对象个数。空间距离和空间对象密度都被考虑在内。这些功能通过考虑空间物体的密度来扩展众所周知的最长公共子序列(LCSS)。
在TSR查询处理中，每个地区都扮演着同样重要的角色，所以我们使用Sigmoid函数归一化空间密度相关性Csd(c,τ)到范围[0，1]。
Sigmoid函数如下：
S(x)＝1/(1+e-x)
代入x＝Csd(c,τ)，S(x)即为空间密度相关性归一化之后的值。
扩展算法中，通过组合每个区域ci∈C的空间密度相关性，一组区域的集合C和轨迹τ之间的空间密度相关性由下面给出：
Figure PCTCN2017113471-appb-000014
Figure PCTCN2017113471-appb-000015
其中，v是轨迹τ上的点，C’sd(c,v)是查询区域c与v之间的空间密度相关性。C’sd(C,v)表示查询区域集合C与轨迹τ的空间密度相关性。pi.g是附属于pi的空间对象的数量。sd(p,v)代表点p与点v之间的距离。*.head表示列表中第一个元素，*.tail表示列表中除head之外的所有元素构成的列表。
以下是本发明基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法(简称BES算法)：
首先，我们利用现有的查询源选择策略(参见S.Shang,K.Zheng,C.S.Jensen,B.Yang,P.Kalnis,G.Li,and J.Wen.Discovery of path nearby clusters in spatial networks.IEEE Trans.Knowl.Data Eng.,27(6):1505–1518,2015.)从查询区域的中心选择一组查询源。其次，我们定义新的空间密度上界和下界来剪枝搜索空间。第三、基于优先级排名的启发式搜索战略调度使用多个查询源。我们保持和使用处理查询时的动态优先级排序堆。在每一个时间点，我们扩展排名最高的查询源，直到一个新的查询源成为顶级。该算法有两大优势：(一)进一步减小了搜索空间，避免重叠区域的遍历；(二)有效启发式搜索策略侧重于那些更容易是解决方案的轨迹，进一步提高查询性能；(三)能有效处理带序列的TSR查询。如图1所示，本发明算法的具体步骤如下：
1、最初，全局空间密度相关性下限LB设置为0，全局空间密度相关性上限UB设置为+∞。
2、我们利用现有的查询源选择策略从查询区域中心中选择一组查询源。现有的查询源选择策略指：给定一组空间对象O(例如，POI，地理标记的照片或地理标记的推文)和查询轨迹q，如果查询源c具有高的空间对象密度并且在空间上接近于q，则返回查询源c。
3、初始所有查询源优先级设置为0。从每个查询源按照基于优先级排名的启发式搜索。我们采用基于优先级排名的启发式调度策略进行Dijkstra扩展算法，可避免将不必要的搜索努力用于不太可能是最佳选择的轨迹。每个查询源pn都有一个标签p.l描述它的优先级。我们在包含这些查询源的p.l上维护一个动态的优先级堆。定义每个查询源p.l的优先级如下:
Figure PCTCN2017113471-appb-000016
其中，p.c是一个包含了查询源p和所有以p为最近查询源的非查询源的查询区域中心的集合，|p.c|是它的大小。Tp是部分覆盖轨迹的集合，Ts(p)是被从p开始的搜索范围覆盖的轨迹集合；C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).ub代表这个相关性的上限。
所有查询源的优先标签设置为0，并在每一步，我们搜索排名最高的查询源(一个最大优先级标签)，按照Dijkstra的算法进行网络扩展。对于每个新扫描的轨迹，如果没有被从p开始的扩展扫描，它被标记为已被p扫描。
4、按照新的公式计算空间密度的上下限，更新LB和UB。按照新的公式计算其空间密度相关性上限C’sd(C,τ).ub和下限C’sd(C,τ).lb，相应更新UB和LB。如果C’sd(C,τ).lb>LB，LB更新为C’sd(C,τ).lb；如果C’sd(C,τ).ub<UB，UB更新为C’sd(C,τ).ub。
BES算法进一步减小了搜索空间，从而避免重叠区域的遍历。查询区域集合C与轨迹τ的空间密度相关性上下界是：
对于查询源，空间密度下限估算公式为：
Figure PCTCN2017113471-appb-000017
对于查询源，空间密度上限估算公式为：
Figure PCTCN2017113471-appb-000018
其中，C是查询区域集合，τ是一条轨迹，C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).lb代表这个相关性的下限，C’sd(C,τ).ub代表这个相关性的上限；C.head表示集合C中第一个查询区域，τ.head表示τ中第一个元素，C’sd(C.head,τ.head).lb表示查询区域C.head与τ.head相关性的下限，C’sd(C.head,τ.head).ub表示查询区域C.head与τ.head相关性的上限，C.tail表示列表中除C.head之外的所有查询区域构成的列表，C’sd(C.tail,τ) 代表查询区域集合C.tail与轨迹τ的相关性，C’sd(C,τ.tail)代表查询区域集合C与轨迹τ.tail的相关性；
对于查询源，空间密度上下界估算公式见上，而对于非查询源的查询区域中心，BES定义了新的查询区域与轨迹空间密度上下界估算公式(以c2，τ1为例)：
Figure PCTCN2017113471-appb-000019
其中，p1是一个查询源，p2是查询区域c2的中心，是一个非查询源，p1是离p2最近的查询源，τ1是一条轨迹。pi.g是附属于pi的空间对象的数量，dM(p1,τ1)代表点p1与轨迹τ1之间的网络距离，sd(pi,p2)代表点pi和点p2之间的网络距离。
Figure PCTCN2017113471-appb-000020
其中，C1表示τ被从c1的中心开始的搜索范围覆盖，C2表示τ没有被从c1的中心开始的搜索范围覆盖。rei表示从ci的中心开始的搜索范围的半径。
5、如果LB>UB或所有搜索半径超过ε+p.dist/2(其中p.dist＝max{sd(p,p’),sd(p,p”)})，p’和p”是p的邻近查询源，sd(p,p’)代表点p和点p’之间的网络距离，sd(p,p”)代表点p和点p”之间的网络距离，ε是事先设置的阈值)，网络的相邻查询源扩展终止，并且Csd(C,τ).ub小于LB的轨迹从Tf移除。Tf是所有被完全覆盖的轨迹的集合。如果p不是排名最高的查询源，网络中从p的扩展终止，我们开始搜索新排名第一的查询源。
6、细化。轨迹在Tf中根据Csd(C,τ).ub的值从最大到最小排序。对于轨迹τ∈Tf，假设{p1,p2,...,pi}是最靠近区域中心{c1.m,c2.m,...,ci.m}的顶点。我们从{p1,p2,...,pi}执行Dijkstra扩展算法来计算pi和区域ci内顶点之间的网络距离。一旦
Figure PCTCN2017113471-appb-000021
(其中Tr是一组细化的轨迹，而Tu是一组未细化的轨迹并且Tr∪Tu＝Tf，τ’是Tu中的一条轨迹)，细化终止，所有未细化的轨迹都被剪枝。返回空间密度相关性最大的轨迹。
图2显示了一个TSR查询实例。如图2所示，c1，c2，c3是TSR查询区域，p1，p2，p3是相应的区域中心，r1、r2和r3是半径。点p3，p4，…，p8是轨迹内的采样点。在轨迹τ1中，p6，p7，p8分别是离中心p1，p2和p3最近的采样点。在轨迹τ2中，p4，p5分别是离中心p1，p2最近的采样点。每个区域包含几个空间对象。只有在对该区域中心的空间接近性被考虑到时，轨迹τ2才被返回，因为轨迹τ2在空间上最接近该地区中心。如果我们考虑空间对象的分布，轨迹τ2则比轨迹τ1缺少吸引力，因为它更远离空间对象密度高的地区。当同时考虑以上两个方面时，轨迹τ1是最好的选择(尽管轨迹τ2是在空间距离上比τ1略好)。
图3显示了空间密度相关性的实施例。以图3为例，τ是一条轨迹，c1和c2是两个区域，p1和p2分别是它们的中心。顶点{p3，p4}∈τ分别是τ上离p1和p2最近的点，{p5,p6,p7,p8}∈c1，{p9，p10}∈c2。空间密度相关性Csd(c1,τ)and Csd(c2,τ)被计算为：Csd(c1,τ)＝ p1·g·I(p1,p3)+p5·g·I(p5,p3)+p6·g·I(p6,p3)+p7·g·I(p7,p3)+p8·g·I(p8,p3)，Csd(c2,τ)＝p2·g·I(p2,p4)+p9·g·I(p9,p4)+p10·g·I(p10,p3)。
图4为本发明一个BES算法实例，τ1已被从p1开始的搜索范围覆盖，p5∈τ1是τ1上最靠近p1的点。因此，τ1被以p1为圆心，dM(p1,τ1)为半径的圆正切，正切点为p5。如果re2＝dM(p1,τ1)-sd(p1,p2)，我们就可以确保圆形区域(p2,re2)被圆形区域(p1,dM(p1,τ1))包围，从而得出dM(p2,τ1)≥re2＝dM(p1,τ1)-sd(p1,p2)。另外，SP(p2,p1)+SP(p1,p5)是从p2到τ1的一条路径，因此得到dM(pm,τ)≤dM(pn,τ)+sd(pm,pn)。我们根据这些关系来确定区域与不同轨迹之间的距离的上下界限从而进行搜索剪枝，并在查询时保持和使用动态优先级排序堆，在每一个时间点，我们扩展排名最高的查询源，直到一个新的查询源成为顶级。
以下通过具体实验来验证本发明的效果：
我们使用从两个空间网络提取的图形，即北京路网(BRN)和北美道路网(NRN)。分别包含28,342个顶点和27,690条边，和17,813个顶点，179,179条边。图形由邻接列表索引。对于BRN，我们使用一个真实的北京出租车的轨迹数据集和实数数据集感兴趣的(空间物体)，其中包含80万个轨迹和30万个POI(兴趣点)。原始POI具有经度和纬度坐标，它们被映射到空间网络，分配给它们最近的顶点。对于BRN中的每个顶点p，我们记录具有其最近顶点的对象的数量。因此，我们不需要在TSR查询处理期间访问个人空间对象。我们与以前的研究分享POI设定[S.Shang,K.Zheng,C.S.Jensen,B.Yang,P.Kalnis,G.Li,and J.Wen.Discovery of path nearby clusters in spatial networks.IEEE Trans.Knowl.Data Eng.,27(6):1505–1518,2015.]。对于NRN，较大的合成数据用于研究可扩展性。NRN包含4,000,000条轨迹。对于NRN中的每个顶点p’，我们得出该数的附加空间物体，我们将这个数字存储为一个属性。我们有180万个派生空间物体。在BRN，默认距离阈值设置在10公里，而在NRN中，默认设置为200公里。所有算法都是在Java中实现并在Windows 8平台上运行，使用英特尔酷睿i7-3520M处理器(2.90GHz)和8GB内存。
默认情况下，BRN中的轨迹集大小设置为600,000，而在NRN设置为1000,000，轨迹长度在BRN中设置为20，在NRN中设置为100，在BRN和BRN中查询区域的数量设置为6。查询区域的平均半径从2公里变化到10公里，在BRN(默认6公里)；在NRN(默认150公里)从50公里到250公里变化。
1.剪枝效果
首先，我们设置实验来查看算法在图上的剪枝效果，实验结果如下：
  BES
剪枝率(BRN) 0.76
保留率(BRN) 0.24
剪枝率(NRN) 0.69
保留率(NRN) 0.31
表1 BES算法的剪枝效果
2.轨迹数的影响
图5给出了不同轨迹的数量|T|下算法的性能。直观地说，一个更大的|T|导致更多的轨迹被处理并产生更大的轨迹搜索空间。因此，本发明算法下的CPU时间和访问轨迹数都将更高。
以上述依据本发明的理想实施例为启示，通过上述的说明内容，相关工作人员完全可以在不偏离本项发明技术思想的范围内，进行多样的变更以及修改。本项发明的技术性范围并不局限于说明书上的内容，必须要根据权利要求范围来确定其技术性范围。

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  1. 一种基于带序兴趣区域的轨迹查询的启发式扩张搜索扩展算法，其特征在于，包括如下步骤：
    步骤1：初始设置全局空间密度相关性下限LB＝0，全局空间密度相关性上限UB＝+∞；定义空间密度相关性计算公式：
    Figure PCTCN2017113471-appb-100001
    Figure PCTCN2017113471-appb-100002
    其中，v是轨迹τ上的点，C’sd(c,v)是查询区域c与v之间的空间密度相关性；C’sd(C,v)表示查询区域集合C与轨迹τ的空间密度相关性；pi。g是附属于pi的空间对象的数量；sd(p,v)代表点p与点v之间的距离；*.head表示列表中第一个元素，*.tail表示列表中除head之外的所有元素构成的列表；
    步骤2：从查询区域中心中选择一组查询源；
    步骤3：所有查询源优先级初始设置为0；从每个查询源按照基于优先级排名进行启发式搜索；
    步骤4：计算空间密度的上限和下限，更新LB和UB；
    步骤5：判断LB>UB或所有搜索半径超过ε+p.dist/2是否成立，其中，ε是事先设置的阈值，p.dist＝max{sd(p,p’),sd(p,p”)}，p’和p”是p的邻近查询源，sd(p,p’)代表点p和点p’之间的网络距离，sd(p,p”)代表点p和点p”之间的网络距离；如成立则网络的相邻查询源扩展终止，进入下一步骤6；如不成立，则回到步骤4；
    步骤6：根据空间密度上限的值对轨迹进行排序；
    步骤7：按照轨迹排序进一步细化，返回具有最大空间密度相关性的轨迹。
  2. 如权利要求1所述的算法，其特征在于，步骤2中，利用查询源选择策略从查询区域中心中选择一组查询源，所述查询源选择策略为：给定一组空间对象O和查询轨迹q，如果查询源c具有高的空间对象密度并且在空间上接近于q，则返回查询源c。
  3. 如权利要求1所述的算法，其特征在于，步骤3中，所述从每个查询源按照基于优先级排名进行启发式搜索具体为：采用基于优先级排名的启发式调度策略进行Dijkstra扩展算法，每个查询源pn都有一个标签p.l描述它的优先级，在包含这些查询源的p.l上维护一个动态的优先级堆，定义每个查询源p.l的优先级如下:
    Figure PCTCN2017113471-appb-100003
    其中，p.c是一个包含了查询源p和所有以p为最近查询源的非查询源的查询区域中心的集合，|p.c|是它的大小。Tp是部分覆盖轨迹的集合，Ts(p)是被从p开始的搜索范围覆盖的轨迹集合；C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).ub代表这个相关性的上限。
  4. 如权利要求1所述的算法，其特征在于，步骤4中，所述计算空间密度的上限和下限具体为：对于每一个新扫描的轨迹，如果没有被从p开始的扩展扫描，它被标记为已被p扫描，计算其空间密度上限C’sd(C,τ).ub和下限C’sd(C,τ).lb；
    对于查询源，空间密度下限估算公式为：
    Figure PCTCN2017113471-appb-100004
    对于查询源，空间密度上限估算公式为：
    Figure PCTCN2017113471-appb-100005
    其中，C是查询区域集合，τ是一条轨迹，C’sd(C,τ)是轨迹τ与查询区域集合C的空间密度相关性，C’sd(C,τ).lb代表这个相关性的下限，C’sd(C,τ).ub代表这个相关性的上限；C.head表示集合C中第一个查询区域，τ.head表示τ中第一个元素，C’sd(C.head,τ.head).lb表示查询区域C.head与τ.head相关性的下限，C’sd(C.head,τ.head).ub表示查询区域C.head与τ.head相关性的上限，C.tail表示列表中除C.head之外的所有查询区域构成的列表，C’sd(C.tail,τ)代表查询区域集合C.tail与轨迹τ的相关性，C’sd(C,τ.tail)代表查询区域集合C与轨迹τ.tail的相关性；
    对于非查询源的查询区域中心，新的查询区域与轨迹空间密度上下界估算公式为，以c2，τ1为例：
    Figure PCTCN2017113471-appb-100006
    其中，p1是一个查询源，p2是查询区域c2的中心，是一个非查询源，p1是离p2最近的查询源，τ1是一条轨迹。pi.g是附属于pi的空间对象的数量，dM(p1,τ1)代表点p1与轨迹τ1之间的网络距离，sd(pi,p2)代表点pi和点p2之间的网络距离。
    Figure PCTCN2017113471-appb-100007
    其中，C1表示τ被从c1的中心开始的搜索范围覆盖，C2表示τ没有被从c1的中心开始的搜索范围覆盖。rei表示从ci的中心开始的搜索范围的半径。
  5. 如权利要求1所述的算法，其特征在于，步骤4中所述更新LB和UB具体为：如果C’sd(C,τ).lb>LB，LB更新为C’sd(C,τ).lb；如果C’sd(C,τ).ub<UB，UB更新为C’sd(C,τ).ub。
  6. 如权利要求1所述的算法，其特征在于，步骤5中所述网络的相邻查询源扩展终止，空间密度上限小于LB的轨迹从Tf中删除，Tf是所有被完全覆盖的轨迹的集合；如果p不是排名最高的查询源，网络中从p的扩展终止，开始搜索新排名第一的查询源。
  7. 如权利要求6所述的算法，其特征在于，步骤6中Tf中的轨迹根据空间密度上限的值排序。
  8. 如权利要求1所述的算法，其特征在于，步骤7中所述按照轨迹排序进一步细化，具体为：对于轨迹τ∈Tf，假设{p1,p2,...,pi}是最靠近区域中心{c1.m,c2.m,...,ci.m}的顶点，从{p1,p2,...,pi}执行Dijkstra扩展算法来计算pi和区域ci内顶点之间的网络距离，一旦
    Figure PCTCN2017113471-appb-100008
    所述细化终止，返回具有最大空 间密度相关性的轨迹；其中Tr是已经被细化的轨迹集合，Tu是未被细化的轨迹集合，Tr∪Tu＝Tf，τ’是Tu中的一条轨迹。
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