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On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Shortest Path and Distance Queries on Road Networks: An Experimental Evaluation
"... Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The stateoftheart solutions for the problem can be divided into two categories: spatialcoherencebased methods and ..."
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Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The stateoftheart solutions for the problem can be divided into two categories: spatialcoherencebased methods and verteximportancebased approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a stateoftheart technique was examined based on a faulty implementation that led to incorrect query results. To address the above issues, this paper presents a comprehensive comparison of the most advanced spatialcoherencebased and verteximportancebased approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios. 1.
Query processing using distance oracles for spatial networks
 Best Papers of ICDE 2009 Special Issue
"... Abstract—The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of spatial oper ..."
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Abstract—The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of spatial operations usually involves the computation of distance along a spatial network instead of “as the crow flies, ” which is not simple. Techniques are described that enable the determination of the network distance between any pair of points (i.e., vertices) with as little as OðnÞ space rather than having to store the n2 distances between all pairs. This is done by being willing to expend a bit more time to achieve this goal such as Oðlog nÞ instead of Oð1Þ, as well as by accepting an error " in the accuracy of the distance that is provided. The strategy that is adopted reduces the space requirements and is based on the ability to identify groups of source and destination vertices for which the distance is approximately the same within some ". The reductions are achieved by introducing a construct termed a distance oracle that yields an estimate of the network distance (termed the "approximate distance) between any two vertices in the spatial network. The distance oracle is obtained by showing how to adapt the wellseparated pair technique from computational geometry to spatial networks. Initially, an "approximate distance oracle of size Oð n " dÞ is used that is capable of retrieving the approximate network distance in Oðlog nÞ time using a Btree. The retrieval time can be theoretically reduced n log n further to Oð1Þ time by proposing another "approximate distance oracle of size Oð
HLDB: Locationbased services in databases
 In Proceedings of the 20th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems (GIS’12), 339–348. ACM Press. Best Paper Award
, 2012
"... This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in stan ..."
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This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in standard SQL. Within the database, HLDB answers exact distance queries and retrieves full shortestpath descriptions in real time, even on networks with tens of millions of vertices. The basic algorithm can be extended in a natural way (still in SQL) to answer much more sophisticated queries, such as finding the ten closest fastfood restaurants. We also introduce efficient new HLbased algorithms for even harder problems, such as best via point, ride sharing, and point of interest prediction. The HLDB framework makes it easy to implement these algorithms in SQL, enabling interactive applications on continental road networks.
ISLABEL: an IndependentSet based Labeling Scheme for PointtoPoint Distance Querying
"... We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 mil ..."
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We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 million vertices, which is rather small in view of many of the fastgrowing realworld graphs today such as social networks and Web graphs. We propose an efficient index, which is a novel labeling scheme based on the independent set of a graph. We show that our method can handle graphs of size orders of magnitude larger than existing indexes. 1.
Continuous Reverse k Nearest Neighbors Queries in . . .
 THE VLDB JOURNAL
"... In this paper, we study the problem of continuous monitoring of reverse ..."
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In this paper, we study the problem of continuous monitoring of reverse
Approximate shortest distance computing: A querydependent local landmark scheme
 In ICDE
, 2012
"... Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an ..."
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Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an embedding. To handle a shortest distance query between two nodes, the precomputed distances from the landmarks to the query nodes are used to compute an approximate shortest distance based on the triangle inequality. In this paper, we analyze the factors that affect the accuracy of the distance estimation in the landmark embedding approach. In particular we find that a globally selected, queryindependent landmark set plus the triangulation based distance estimation introduces a large relative error, especially for nearby query nodes. To address this issue, we propose a querydependent local landmark scheme, which identifies a local landmark close to the specific query nodes and provides a more accurate distance estimation than the traditional global landmark approach. Specifically, a local landmark is defined as the least common ancestor of the two query nodes in the shortest path tree rooted at a global landmark. We propose efficient local landmark indexing and retrieval techniques, which are crucial to achieve low offline indexing complexity and online query complexity. Two optimization techniques on graph compression and graph online search are also proposed, with the goal to further reduce index size and improve query accuracy. Our experimental results on largescale social networks and road networks demonstrate that the local landmark scheme reduces the shortest distance estimation error significantly when compared with global landmark embedding. I.
Hop Doubling Label Indexing for PointtoPoint Distance Querying on ScaleFree Networks
"... We study the problem of pointtopoint distance querying for massive scalefree graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a novel hopdoubling labeling technique. We derive bounds on th ..."
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We study the problem of pointtopoint distance querying for massive scalefree graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a novel hopdoubling labeling technique. We derive bounds on the index size, the computation costs and I/O costs based on the properties of unweighted scalefree graphs. We show that our method is much more efficient and effective compared to the stateoftheart techniques, in terms of both querying time and indexing costs. Our empirical study shows that our method can handle graphs that are orders of magnitude larger than existing methods. 1.
Roads Belong in Databases
"... The popularity of locationbased services and the need to perform realtime processing on them has led to an interest in queries on road networks, such as finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of operations usually involves the compu ..."
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The popularity of locationbased services and the need to perform realtime processing on them has led to an interest in queries on road networks, such as finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of operations usually involves the computation of distance along a spatial network instead of “as the crow flies, ” which is not simple. This requires the precomputation of the shortest paths and network distance between every pair of points (i.e., vertices) with as little space as possible rather than having to store the n 2 shortest paths and distances between all pairs. This problem is related to a ‘holy grail ’ problem in databases of how to incorporate road networks into relational databases. A data structure called a road network oracle is introduced that resides in a database and enables the processing of many operations on road networks with just the aid of relational operators. Two implementations of road network oracles are presented. 1
Towards online shortest path computation
 IEEE Trans. Knowl. Data Eng
, 2014
"... Abstract—The online shortest path problem aims at computing the shortest path based on live traffic circumstances. This is very important in modern car navigation systems as it helps drivers to make sensible decisions. To our best knowledge, there is no efficient system/solution that can offer affor ..."
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Abstract—The online shortest path problem aims at computing the shortest path based on live traffic circumstances. This is very important in modern car navigation systems as it helps drivers to make sensible decisions. To our best knowledge, there is no efficient system/solution that can offer affordable costs at both client and server sides for online shortest path computation. Unfortunately, the conventional clientserver architecture scales poorly with the number of clients. A promising approach is to let the server collect live traffic information and then broadcast them over radio or wireless network. This approach has excellent scalability with the number of clients. Thus, we develop a new framework called live traffic index (LTI) which enables drivers to quickly and effectively collect the live traffic information on the broadcasting channel. An impressive result is that the driver can compute/update their shortest path result by receiving only a small fraction of the index. Our experimental study shows that LTI is robust to various parameters and it offers relatively short tunein cost (at client side), fast query response time (at client side), small broadcast size (at server side), and light maintenance time (at server side) for online shortest path problem. Index Terms—Spatial databases; Vehicle driving; Broadcasting F