Optimal location queries in road network databases
11 Apr 2011-pp 804-815
TL;DR: A unified framework is proposed that addresses three variants of OL queries that find important applications in practice, and is instantiate the framework with several novel query processing algorithms.
Abstract: Optimal location (OL) queries are a type of spatial queries particularly useful for the strategic planning of resources. Given a set of existing facilities and a set of clients, an OL query asks for a location to build a new facility that optimizes a certain cost metric (defined based on the distances between the clients and the facilities). Several techniques have been proposed to address OL queries, assuming that all clients and facilities reside in an L p space. In practice, however, movements between spatial locations are usually confined by the underlying road network, and hence, the actual distance between two locations can differ significantly from their L p distance. Motivated by the deficiency of the existing techniques, this paper presents the first study on OL queries in road networks. We propose a unified framework that addresses three variants of OL queries that find important applications in practice, and we instantiate the framework with several novel query processing algorithms. We demonstrate the efficiency of our solutions through extensive experiments with real data.
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01 Jul 2012
TL;DR: In this paper, a scalable external-memory algorithm (ExactMaxRS) was proposed for the MaxCRS problem, which is optimal in terms of the I/O complexity.
Abstract: This paper investigates the MaxRS problem in spatial databases. Given a set O of weighted points and a rectangular region r of a given size, the goal of the MaxRS problem is to find a location of r such that the sum of the weights of all the points covered by r is maximized. This problem is useful in many location-based applications such as finding the best place for a new franchise store with a limited delivery range and finding the most attractive place for a tourist with a limited reachable range. However, the problem has been studied mainly in theory, particularly, in computational geometry. The existing algorithms from the computational geometry community are in-memory algorithms which do not guarantee the scalability. In this paper, we propose a scalable external-memory algorithm (ExactMaxRS) for the MaxRS problem, which is optimal in terms of the I/O complexity. Furthermore, we propose an approximation algorithm (ApproxMaxCRS) for the MaxCRS problem that is a circle version of the MaxRS problem. We prove the correctness and optimality of the ExactMaxRS algorithm along with the approximation bound of the ApproxMaxCRS algorithm. From extensive experimental results, we show that the ExactMaxRS algorithm is two orders of magnitude faster than methods adapted from existing algorithms, and the approximation bound in practice is much better than the theoretical bound of the ApproxMaxCRS algorithm.
65 citations
01 Apr 2012
TL;DR: A novel method is proposed, which has very close performance to the fastest method but does not need an extra index, and a detailed comparative cost analysis on the various algorithms is provided.
Abstract: We propose and study a new type of location optimization problem: given a set of clients and a set of existing facilities, we select a location from a given set of potential locations for establishing a new facility so that the average distance between a client and her nearest facility is minimized. We call this problem the min-dist location selection problem, which has a wide range of applications in urban development simulation, massively multiplayer online games, and decision support systems. We explore two common approaches to location optimization problems and propose methods based on those approaches for solving this new problem. However, those methods either need to maintain an extra index or fall short in efficiency. To address their drawbacks, we propose a novel method (named MND), which has very close performance to the fastest method but does not need an extra index. We provide a detailed comparative cost analysis on the various algorithms. We also perform extensive experiments to evaluate their empirical performance and validate the efficiency of the MND method.
63 citations
Cites background or methods or result from "Optimal location queries in road ne..."
...Similarly, the endpoints of the edges in E [17] are different from the points in P....
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...[17] study the min-dist problem in road networks....
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...Solution Distance Datasets Function Space Function [1] Max-inf Continuous L2 C, F [2] Max-inf Discrete L2 C, F [14] Max-inf Continuous L1 C, F [15] Max-inf Discrete L2 C, P [16] Max-inf Discrete L2 C, F , P [3] Min-dist Continuous L1 C, F [17] Min-dist Continuous Network C, F , E [4] Min-dist Discrete L2 C, P Proposed Min-dist Discrete L2 C, F , P...
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...These two studies [3], [17] have the same min-dist optimization function as ours, but our study has a set P, the potential locations given as candidates for selection....
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18 Jun 2014
TL;DR: This paper proposes an efficient algorithm for the optimal location query problem, which is based on a novel idea of \emph{nearest location component}.
Abstract: In this paper, we study the optimal location query problem based on road networks. Specifically, we have a road network on which some clients and servers are located. Each client finds the server that is closest to her for service and her cost of getting served is equal to the (network) distance between the client and the server serving her multiplied by her weight or importance. The optimal location query problem is to find a location for setting up a new server such that the maximum cost of clients being served by the servers (including the new server) is minimized. This problem has been studied before, but the state-of-the-art is still not efficient enough. In this paper, we propose an efficient algorithm for the optimal location query problem, which is based on a novel idea of \emph{nearest location component}. We also discuss three extensions of the optimal location query problem, namely the optimal multiple-location query problem, the optimal location query problem on 3D road networks, and the optimal location query problem with another objective. Extensive experiments were conducted which showed that our algorithms are faster than the state-of-the-art by at least an order of magnitude on large real benchmark datasets. For example, on our largest real datasets, the state-of-the-art ran for more than 10 hours but our algorithm ran within 3 minutes only (i.e., >200 times faster).
62 citations
01 Aug 2013
TL;DR: The present paper studies the (1 - e)-approximate MaxRS problem, which admits the same inputs as MaxRS, but aims instead to return a rectangle whose covered weight is at least (1-e)m*, where m* is the optimal covered weight, and e can be an arbitrarily small constant between 0 and 1.
Abstract: In the maximizing range sum (MaxRS) problem, given (i) a set P of 2D points each of which is associated with a positive weight, and (ii) a rectangle r of specific extents, we need to decide where to place r in order to maximize the covered weight of r - that is, the total weight of the data points covered by r. Algorithms solving the problem exactly entail expensive CPU or I/O cost. In practice, exact answers are often not compulsory in a MaxRS application, where slight imprecision can often be comfortably tolerated, provided that approximate answers can be computed considerably faster. Motivated by this, the present paper studies the (1 - e)-approximate MaxRS problem, which admits the same inputs as MaxRS, but aims instead to return a rectangle whose covered weight is at least (1-e)m*, where m* is the optimal covered weight, and e can be an arbitrarily small constant between 0 and 1. We present fast algorithms that settle this problem with strong theoretical guarantees.
50 citations
Cites background from "Optimal location queries in road ne..."
...Indeed, the consequence is that either the algorithm will fail to achieve the purpose, or S is such a large sample set that its size is already at the scale of P ....
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14 Jun 2016
TL;DR: This paper introduces a novel problem called the best region search (BRS) problem and provides efficient solutions to it and proposes an efficient algorithm called SliceBRS to find the exact answer and proves that the answer found by it is bounded by a constant.
Abstract: The increasing popularity and growth of mobile devices and location-based services enable us to utilize large-scale geo-tagged data to support novel location-based applications. This paper introduces a novel problem called the best region search (BRS) problem and provides efficient solutions to it. Given a set O of spatial objects, a submodular monotone aggregate score function, and the size a x b of a query rectangle, the BRS problem aims to find a x b rectangular region such that the aggregate score of the spatial objects inside the region is maximized. This problem is fundamental to support several real-world applications such as most influential region search (eg. the best location for a signage to attract most audience) and most diversified region search (eg. region with most diverse facilities). We propose an efficient algorithm called SliceBRS to find the exact answer to the BRS problem. Furthermore, we propose an approximate solution called CoverBRS and prove that the answer found by it is bounded by a constant. Our experimental study with real-world datasets and applications demonstrates the effectiveness and superiority of our proposed algorithms.
44 citations
Cites background from "Optimal location queries in road ne..."
...The problem is also considered in the context of road networks [5, 28] with road network distance....
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References
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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
"Optimal location queries in road ne..." refers methods in this paper
...Blossom has an O(n(2) log n) time complexity, since it invokes Dijkstra’s algorithm once for each client, and each execution of Dijkstra’s algorithm takes O(n log n) time in the worst case [22]....
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...we apply Dijkstra’s algorithm [22] to traverse the vertices in G in ascending order of their distances to c....
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Book•
01 Jan 1997TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
Abstract: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
4,805 citations
09 Sep 2003
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.
675 citations
"Optimal location queries in road ne..." refers background in this paper
...Lastly, there is a large body of literature on query processing techniques for road network databases [9]–[18]....
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...Most of those techniques are designed for the nearest neighbor (NN) query [9], [10], [16] or its variants, e....
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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
Additional excerpts
...Most of those techniques are designed for the nearest neighbor (NN) query [9], [10], [16] or its variants, e....
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TL;DR: The method can be used to compute the upper envelope of “segments” that intersect pairwise at most k times and computes theupper envelope in O(λk + 1(n)log n) time.
325 citations
"Optimal location queries in road ne..." refers background in this paper
...As there exist O(n) segments in R, the upper envelope gup should contain O(n) linear pieces, and can be computed in O(n log n) time and O(n) space [20]....
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