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40
PHAST: hardwareaccelerated shortest path trees
 J. PARALLEL DISTRIB. COMPUT
, 2013
"... We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Becaus ..."
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Cited by 20 (4 self)
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We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Because this sweep is independent of the source, we are able to reorder vertices in advance to exploit locality. Moreover, our algorithm takes advantage of features of modern CPU architectures, such as SSE and multiple cores. Compared to Dijkstra’s algorithm, our method needs fewer operations, has better locality, and is better able to exploit parallelism at multicore and instruction levels. We gain additional speedup when implementing our algorithm on a GPU, where it is up to three orders of magnitude faster than Dijkstra’s algorithm on a highend CPU. This makes applications based on allpairs shortestpaths practical for continentalsized road networks. Several algorithms, such as computing the graph diameter, arc flags, or exact reaches, can be greatly accelerated by our method.
VCdimension and shortest path algorithms
"... We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the p ..."
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Cited by 17 (5 self)
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We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the pointtopoint shortest path problem in networks of low highway dimension, such as road networks. We also refine the definitions of highway dimension and related concepts, making them more general and potentially more relevant to practice. In particular, we define highway dimension in terms of set systems induced by shortest paths, and give cardinalitybased and average case definitions.
Efficient Processing of Distance Queries in Large Graphs: A Vertex Cover Approach
, 2012
"... We propose a novel diskbased index for processing singlesource shortest path or distance queries. The index is useful in a wide range of important applications (e.g., network analysis, routing planning, etc.). Our index is a treestructured index constructed based on the concept of vertex cover. W ..."
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Cited by 14 (4 self)
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We propose a novel diskbased index for processing singlesource shortest path or distance queries. The index is useful in a wide range of important applications (e.g., network analysis, routing planning, etc.). Our index is a treestructured index constructed based on the concept of vertex cover. We propose an I/Oefficient algorithm to construct the index when the input graph is too large to fit in main memory. We give detailed analysis of I/O and CPU complexity for both index construction and query processing, and verify the efficiency of our index for query processing in massive realworld graphs.
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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Cited by 11 (0 self)
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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 11 (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.
Exact Distance Oracles for Planar Graphs
, 2010
"... We provide the first linearspace data structure with provable sublinear query time for exact pointtopoint shortest path queries in planar graphs. We prove that for any planar graph G with nonnegative arc lengths and for any ɛ> 0 there is a data structure that supports exact shortest path and d ..."
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Cited by 9 (5 self)
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We provide the first linearspace data structure with provable sublinear query time for exact pointtopoint shortest path queries in planar graphs. We prove that for any planar graph G with nonnegative arc lengths and for any ɛ> 0 there is a data structure that supports exact shortest path and distance queries in G with the following properties: the data structure can be created in time O(n lg(n) lg(1/ɛ)), the space required is O(n lg(1/ɛ)), and the query time is O(n 1/2+ɛ). Previous data structures by Fakcharoenphol and Rao (JCSS’06), Klein, Mozes, and Weimann (TransAlg’10), and Mozes and WulffNilsen (ESA’10) with query time O(n 1/2 lg 2 n) use space at least Ω(n lg n / lg lg n). We also give a construction with a more general tradeoff. We prove that for any integer S ∈ [n lg n, n 2], we can construct in time Õ(S) a data structure of size O(S) that answers distance queries in O(nS −1/2 lg 2.5 n) time per query. Cabello (SODA’06) gave a comparable construction for the smaller range S ∈ [n 4/3 lg 1/3 n, n 2]. For the range S ∈ (n lg n, n 4/3 lg 1/3 n), only data structures of size O(S) with query time O(n 2 /S) had been known (Djidjev, WG’96). Combined, our results give the best query times for any shortestpath data structure for planar graphs with space S = o(n 4/3 lg 1/3 n). As a consequence, we also obtain an algorithm that computes k–many distances in planar graphs in time O((kn) 2/3 (lg n) 2 (lg lg n) −1/3 + n(lg n) 2 / lg lg n). 1
UserConstrained MultiModal Route Planning
"... In the multimodal route planning problem we are given multiple transportation networks (e. g., pedestrian, road, public transit) and ask for a best integrated journey between two points. The main challenge is that a seemingly optimal journey may have changes between networks that do not reflect the ..."
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Cited by 8 (1 self)
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In the multimodal route planning problem we are given multiple transportation networks (e. g., pedestrian, road, public transit) and ask for a best integrated journey between two points. The main challenge is that a seemingly optimal journey may have changes between networks that do not reflect the user’s modal preferences. In fact, quickly computing reasonable multimodal routes remains a challenging problem: Previous approaches either suffer from poor query performance or their available choices of modal preferences during query time is limited. In this work we focus on computing exact multimodal journeys that can be restricted by specifying arbitrary modal sequences at query time. For example, a user can say whether he wants to only use public transit, or also prefers to use a taxi or walking at the beginning or end of the journey; or if he has no restrictions at all. By carefully adapting node contraction, a common ingredient to many speedup techniques on road networks, we are able to compute pointtopoint queries on a continental network combined of cars, railroads and flights several orders of magnitude faster than Dijkstra’s algorithm. Thereby, we require little space overhead and obtain fast preprocessing times.
Scaleinvariant random spatial networks
"... Realworld road networks have an approximate scaleinvariance property; can one devise mathematical models of random networks whosedistributionsareexactlyinvariantunderEuclideanscaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call scale ..."
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Cited by 7 (5 self)
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Realworld road networks have an approximate scaleinvariance property; can one devise mathematical models of random networks whosedistributionsareexactlyinvariantunderEuclideanscaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call scaleinvariant random spatial networks, whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimumtime routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class.
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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Cited by 7 (2 self)
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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.
Efficient data management in support of shortestpath computation
 In Proceedings of the 4th ACM SIGSPATIAL International Workshop on Computational Transportation Science, CTS ’11
, 2011
"... While many efficient proposals exist for solving the singlepair shortestpath problem, a solution that sees the algorithmic solution in combination with efficient data management has received considerably little attention. This work proposes a data management approach for efficient shortest path co ..."
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Cited by 5 (4 self)
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While many efficient proposals exist for solving the singlepair shortestpath problem, a solution that sees the algorithmic solution in combination with efficient data management has received considerably little attention. This work proposes a data management approach for efficient shortest path computation that exploits road network hierarchies. Hierarchies allow us to minimize the portion of the network that is kept in main memory. This approach is insensitive to changes to the network as it does not rely on any precomputation, but only on given road network properties. In that we specifically target large road networks that exhibit a high degree of change (e.g., OpenStreetMap). Extensive experimental evaluation shows that the presented solution is both efficient and scalable and provides competitive shortestpath computation performance without requiring a preprocessing stage for the road network graph.