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12
TimeDependent Route Planning
 Robust and Online LargeScale Optimization, LNCS
, 2009
"... Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmen ..."
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Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmented to guarantee correctness in timedependent networks. With the ingredients adapted, three efficient speedup techniques can be set up: CoreALT, SHARC, and Contraction Hierarchies. Experiments on realworld data deriving from road networks and public transportation confirm that these techniques allow the fast computation of timedependent shortest paths. 1
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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Cited by 9 (0 self)
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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.
Chromatic Correlation Clustering
"... We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges are of different types (colors). We introduce an objective function that aims at partitioning the graph such that the edge ..."
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Cited by 4 (3 self)
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We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges are of different types (colors). We introduce an objective function that aims at partitioning the graph such that the edges within each cluster have, as much as possible, the same color. We show that the problem is NPhard and propose a randomized algorithm with approximation guarantee proportional to the maximum degree of the input graph. The algorithm iteratively picks a random edge as pivot, builds a cluster around it, and removes the cluster from the graph. Although being fast, easytoimplement, and parameter free, this algorithm tends to produce a relatively large number of clusters. To overcome this issue we introduce a variant algorithm, which modifies how the pivot is chosen and and how the cluster is built around the pivot. Finally, to address the case where a fixed number of output clusters is required, we devise a third algorithm that directly optimizes the objective function via a strategy based on the alternating minimization paradigm. We test our algorithms on synthetic and real data from the domains of proteininteraction networks, social media, and bibliometrics. Experimental evidence show that our algorithms outperform a baseline algorithm both in the task of reconstructing a groundtruth clustering and in terms of objective function value.
TAREEG: A MapReduceBased System for Extracting Spatial Data from OpenStreetMap
"... Real spatial data, e.g., detailed road networks, rivers, buildings, parks, are not easily available for most of the world. This hinders the practicality of many research ideas that need a real spatial data for testing and experiments. Such data is often available for governmental use, or at major s ..."
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Real spatial data, e.g., detailed road networks, rivers, buildings, parks, are not easily available for most of the world. This hinders the practicality of many research ideas that need a real spatial data for testing and experiments. Such data is often available for governmental use, or at major software companies, but it is prohibitively expensive to build or buy for academia or individual researchers. This paper presents TAREEG; a webservice that makes real spatial data, from anywhere in the world, available at the fingertips of every researcher or individual. TAREEG gets all its data by leveraging the richness of OpenStreetMap data set; the most comprehensive available spatial data of the world. Yet, it is still challenging to obtain OpenStreetMap data due to the size limitations, special data format, and the noisy nature of spatial data. TAREEG employs MapReducebased techniques to make it efficient and easy to extract OpenStreetMap data in a standard form with minimal effort. Experimental results show that TAREEG is highly accurate and efficient.
Distance oracles in edgelabeled graphs
"... A fundamental operation over edgelabeled graphs is the computation of shortestpath distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance com ..."
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A fundamental operation over edgelabeled graphs is the computation of shortestpath distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance computation is used as a primitive for more complex computations. In this paper we study the problem of efficient approximation of shortestpath queries with edgelabel constraints, for which we devise two indexes based on the idea of landmarks: distances from all vertices of the graph to a selected subset of landmark vertices are precomputed and then used at query time to efficiently approximate distance queries. The major challenge to face is that, in principle, an exponential number of constraint label sets needs to be stored for each vertexlandmark pair, which makes the index precomputation and storage far from trivial. We tackle this challenge from two different perspectives, which lead to indexes with different characteristics: one index is faster and more accurate, but it requires more space than the other. We extensively evaluate our techniques on real and synthetic datasets, showing that our indexes can efficiently and accurately estimate labelconstrained distance queries. 1.
DOI 10.1007/s007780120274x REGULAR PAPER The exact distance to destination in undirected world
"... Abstract Shortest distance queries are essential not only in graph analysis and graph mining tasks but also in database applications, when a large graph needs to be dealt with. Such shortest distance queries are frequently issued by endusers or requested as a subroutine in real applications. For in ..."
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Abstract Shortest distance queries are essential not only in graph analysis and graph mining tasks but also in database applications, when a large graph needs to be dealt with. Such shortest distance queries are frequently issued by endusers or requested as a subroutine in real applications. For intensive queries on large graphs, it is impractical to compute shortest distances online from scratch, and impractical to materialize allpairs shortest distances. In the literature, 2hop distance labeling is proposed to index the allpairs shortest distances. It assigns distance labels to vertices in a large graph in a precomputing step offline and then answers shortest distance queries online by making use of such distance labels, which avoids exhaustively traversing the large graph when answering queries. However, the existing algorithms to generate 2hop distance labels are not scalable to large graphs. Finding an optimal 2hop distance labeling is NPhard, and heuristic algorithms may generate large size distance labels while still needing to precompute allpairs shortest paths. In this paper, we propose a multihop distance labeling approach, which generates a subset of the 2hop distance labels as index offline. We can compute the multihop distance labels efficiently by avoiding precomputing allpairs shortest paths. In addition, our multihop distance labeling is small in size to be
CANDS: Continuous Optimal Navigation via Distributed Stream Processing ∗
"... Shortest path query over a dynamic road network is a prominent problem for the optimization of realtime traffic systems. Existing solutions rely either on a centralized index system with tremendous precomputation overhead, or on a distributed graph processing system such as Pregel that requires ..."
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Shortest path query over a dynamic road network is a prominent problem for the optimization of realtime traffic systems. Existing solutions rely either on a centralized index system with tremendous precomputation overhead, or on a distributed graph processing system such as Pregel that requires much synchronization effort. However, the performance of these systems degenerates with frequent route path updates caused by continuous traffic condition change. In this paper, we build CANDS, a distributed stream processing platform for continuous optimal shortest path queries. It provides an asynchronous solution to answering a large quantity of shortest path queries. It is able to efficiently detect affected paths and adjust their paths in the face of traffic updates. Moreover, the affected paths can be quickly updated to the optimal solutions throughout the whole navigation process. Experimental results demonstrate that the performance for answering shortest path queries by CANDS is two orders of magnitude better than that of GPS, an opensource implementation of Pregel. In addition, CANDS provides fast response to traffic updates to guarantee the optimality of answering shortest path queries. 1.
Realtime Response of Shortest Path Computation
"... Computing the shortest path between two locations in a network is an important and fundamental problem that finds applications in a wide range of fields. This problem has attracted considerable research interest and led to a plethora of algorithms. However, existing approaches have two main drawba ..."
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Computing the shortest path between two locations in a network is an important and fundamental problem that finds applications in a wide range of fields. This problem has attracted considerable research interest and led to a plethora of algorithms. However, existing approaches have two main drawbacks: complete path computation before movement and reprocessing when node failure occurs. In this paper, two novel algorithms, RSP (Realtime Shortest Path) and RSP+ (Realtime Shortest Path Plus), are proposed to handle both shortcomings. We perform a network preprocessing to ensure a constant time response of retrieving the shortest route for an arbitrary node to an important set of destinations. RSP+ further divides the complete path into smaller partial paths, which can then be computed in parallel. Besides, considering the continuous changes of the network, like traffic jams and road constructions, where certain paths are blocked, a fast recovery method to efficiently find the best alternative route is integrated into RSP+. Empirical studies have shown that RSP+ can achieve an average query processing time of 0.8 microseconds. Besides, the effectiveness of the recovery mechanism demonstrates that alternative routes can be obtained to avoid unavailable areas.