Query processing in spatial network databases
09 Sep 2003-pp 802-813
TL;DR: A Euclidean restriction and a network expansion framework that take advantage of location and connectivity to efficiently prune the search space are developed and applied to the most popular spatial queries.
Abstract: Despite the importance of spatial networks in real-life applications, most of the spatial database literature focuses on Euclidean spaces. In this paper we propose an architecture that integrates network and Euclidean information, capturing pragmatic constraints. Based on this architecture, we develop a Euclidean restriction and a network expansion framework that take advantage of location and connectivity to efficiently prune the search space. These frameworks are successfully applied to the most popular spatial queries, namely nearest neighbors, range search, closest pairs and e-distance joins, in the context of spatial network databases.
Citations
More filters
31 Aug 2004
TL;DR: This paper proposes a novel approach to efficiently and accurately evaluate KNN queries in spatial network databases using first order Voronoi diagram, which outperforms approaches that are based on on-line distance computation by up to one order of magnitude, and provides a factor of four improvement in the selectivity of the filter step as compared to the index-based approaches.
Abstract: A frequent type of query in spatial networks (e.g., road networks) is to find the K nearest neighbors (KNN) of a given query object. With these networks, the distances between objects depend on their network connectivity and it is computationally expensive to compute the distances (e.g., shortest paths) between objects. In this paper, we propose a novel approach to efficiently and accurately evaluate KNN queries in spatial network databases using first order Voronoi diagram. This approach is based on partitioning a large network to small Voronoi regions, and then pre-computing distances both within and across the regions. By localizing the precomputation within the regions, we save on both storage and computation and by performing across-the-network computation for only the border points of the neighboring regions, we avoid global pre-computation between every node-pair. Our empirical experiments with several real-world data sets show that our proposed solution outperforms approaches that are based on on-line distance computation by up to one order of magnitude, and provides a factor of four improvement in the selectivity of the filter step as compared to the index-based approaches.
520 citations
Cites background or methods from "Query processing in spatial network..."
...See the full-paper or [9] for details....
[...]
...Table 1 shows the results of comparing query response time between VN(3) and the INE approach proposed in [9]....
[...]
...in [9] propose a solution for nearest neighbor queries in network databases by introducing an architecture that integrates network and Euclidean information and captures pragmatic constraints....
[...]
...With this approach, we use a method similar to what proposed in [9] to find the distance between q and BoP (NV P (q))....
[...]
..., [9]) with the advantage that the network expansion only explores the objects that are closer to q and computes their distances to q during expansion....
[...]
22 Aug 2005
TL;DR: This paper provides a number of approximation algorithms with approximation ratios that depend on either the number of categories, the maximum number of points per category or both, and gives an experimental evaluation of the proposed algorithms using both synthetic and real datasets.
Abstract: In this paper we discuss a new type of query in Spatial Databases, called the Trip Planning Query (TPQ). Given a set of points of interest P in space, where each point belongs to a specific category, a starting point S and a destination E, TPQ retrieves the best trip that starts at S, passes through at least one point from each category, and ends at E. For example, a driver traveling from Boston to Providence might want to stop to a gas station, a bank and a post office on his way, and the goal is to provide him with the best possible route (in terms of distance, traffic, road conditions, etc.). The difficulty of this query lies in the existence of multiple choices per category. In this paper, we study fast approximation algorithms for TPQ in a metric space. We provide a number of approximation algorithms with approximation ratios that depend on either the number of categories, the maximum number of points per category or both. Therefore, for different instances of the problem, we can choose the algorithm with the best approximation ratio, since they all run in polynomial time. Furthermore, we use some of the proposed algorithms to derive efficient heuristics for large datasets stored in external memory. Finally, we give an experimental evaluation of the proposed algorithms using both synthetic and real datasets.
312 citations
Cites background or methods from "Query processing in spatial network..."
...Nearest neighbor queries on road networks have been studied in [27], where a simple extension of the well known Dijkstra algorithm [10] for the single-source shortest-path problem on weighted graphs is utilized to locate the nearest point of interest to a given query point....
[...]
...Spatial databases has been an active area of research in the last two decades and many important results in data modeling, spatial indexing, and query processing techniques have been reported [29, 17, 40, 37, 42, 26, 36, 4, 18, 27]....
[...]
...As with the R-tree case, straightforwardly, we can utilize the algorithm of [27] to incrementally locate the nearest neighbor of the last stop added to the trip, that belongs to a category that has not been visited yet....
[...]
...For our purposes we represent the road network using techniques from [32, 43, 27]....
[...]
...Recent papers that extend various types of queries to spatial networks are [27, 21, 30]....
[...]
09 Jun 2008
TL;DR: The algorithm and underlying representation of the shortest paths in the spatial network can be used with different sets of objects, and the amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree.
Abstract: An algorithm is presented for finding the k nearest neighbors in a spatial network in a best-first manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as well as a theoretical analysis have shown that the storage has been reduced from O(N3) to O(N1.5) (i.e., by an order of magnitude equal to the square root). The precomputation of the shortest paths along the network essentially decouples the process of computing shortest paths along the network from that of finding the neighbors, and thereby also decouples the domain S of the query objects and that of the objects from which the neighbors are drawn from the domain V of the vertices of the spatial network. This means that as long as the spatial network is unchanged, the algorithm and underlying representation of the shortest paths in the spatial network can be used with different sets of objects.
310 citations
18 Feb 2012
TL;DR: In this article, the authors published a journal article entitled "Journal of Modern Foreign Psychology 2018, vol. 7, no. 2, pp. 90 and 99, with the following abstracts:
Abstract: © 2018 ФГБОУ ВО МГППУ «Московский государственный психолого-педагогический университет» © 2018 Moscow State University of Psychology & Education E-journal «Journal of Modern Foreign Psychology» 2018, vol. 7, no. 2, pp. 90—99. doi: 10.17759/jmfp.2018070209 ISSN: 2304-4977 (online) Электронный журнал «Современная зарубежная психология» 2018. Том 7. No 2. С. 90—99. doi: 10.17759/jmfp.2018070209 ISSN: 2304-4977 (online)
289 citations
Additional excerpts
...Στο [13] οι συγγραφείς μελετούν την επεξεργασία ερωτημάτων σε στατικά σύνολα δεδομένων, χρησιμοποιώντας και μία γραφική αναπαράσταση του δικτύου και μία μέθοδο χωρικής προσπέλασης....
[...]
TL;DR: If Q fits in memory and
Abstract: Given two spatial datasets P (eg, facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q Assuming, for example, n users at locations q1,…qn, an ANN query outputs the facility p ∈ P that minimizes the sum of distances vpqiv for 1 ≤ i ≤ n that the users have to travel in order to meet there Similarly, another ANN query may report the point p ∈ P that minimizes the maximum distance that any user has to travel, or the minimum distance from some user to his/her closest facility If Q fits in memory and P is indexed by an R-tree, we develop algorithms for aggregate nearest neighbors that capture several versions of the problem, including weighted queries and incremental reporting of results Then, we analyze their performance and propose cost models for query optimization Finally, we extend our techniques for disk-resident queries and approximate ANN retrieval The efficiency of the algorithms and the accuracy of the cost models are evaluated through extensive experiments with real and synthetic datasets
283 citations
References
More filters
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Abstract: We consider n points (nodes), some or all pairs of which are connected by a branch; the length of each branch is given. We restrict ourselves to the case where at least one path exists between any two nodes. We now consider two problems. Problem 1. Constrnct the tree of minimum total length between the n nodes. (A tree is a graph with one and only one path between every two nodes.) In the course of the construction that we present here, the branches are subdivided into three sets: I. the branches definitely assignec~ to the tree under construction (they will form a subtree) ; II. the branches from which the next branch to be added to set I, will be selected ; III. the remaining branches (rejected or not yet considered). The nodes are subdivided into two sets: A. the nodes connected by the branches of set I, B. the remaining nodes (one and only one branch of set II will lead to each of these nodes), We start the construction by choosing an arbitrary node as the only member of set A, and by placing all branches that end in this node in set II. To start with, set I is empty. From then onwards we perform the following two steps repeatedly. Step 1. The shortest branch of set II is removed from this set and added to
22,704 citations
Book•
01 Jan 1990TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher:
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects.
In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage.
As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds.
Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.
21,651 citations
01 Jun 1984
TL;DR: A dynamic index structure called an R-tree is described which meets this need, and algorithms for searching and updating it are given and it is concluded that it is useful for current database systems in spatial applications.
Abstract: In order to handle spatial data efficiently, as required in computer aided design and geo-data applications, a database system needs an index mechanism that will help it retrieve data items quickly according to their spatial locations However, traditional indexing methods are not well suited to data objects of non-zero size located m multi-dimensional spaces In this paper we describe a dynamic index structure called an R-tree which meets this need, and give algorithms for searching and updating it. We present the results of a series of tests which indicate that the structure performs well, and conclude that it is useful for current database systems in spatial applications
7,336 citations
01 May 1990
TL;DR: The R*-tree is designed which incorporates a combined optimization of area, margin and overlap of each enclosing rectangle in the directory which clearly outperforms the existing R-tree variants.
Abstract: The R-tree, one of the most popular access methods for rectangles, is based on the heuristic optimization of the area of the enclosing rectangle in each inner node. By running numerous experiments in a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which incorporates a combined optimization of area, margin and overlap of each enclosing rectangle in the directory. Using our standardized testbed in an exhaustive performance comparison, it turned out that the R*-tree clearly outperforms the existing R-tree variants. Guttman's linear and quadratic R-tree and Greene's variant of the R-tree. This superiority of the R*-tree holds for different types of queries and operations, such as map overlay, for both rectangles and multidimensional points in all experiments. From a practical point of view the R*-tree is very attractive because of the following two reasons 1 it efficiently supports point and spatial data at the same time and 2 its implementation cost is only slightly higher than that of other R-trees.
4,686 citations
24 May 1994
TL;DR: An efficient indexing method to locate 1-dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance.
Abstract: We present an efficient indexing method to locate 1-dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequences into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more detail, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.
1,750 citations