Shortest-path queries in static networks

Sommer, Christian

doi:10.1145/2530531

Cited by 194 publications

(100 citation statements)

References 175 publications

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“…While the problem can be solved by Dijkstra's algorithm [16], it is too slow in practice. Therefore, a multitude of speedup techniques use an offline preprocessing phase to accelerate queries (see [11,32] for surveys). Most were developed for static arc costs representing travel times.…”

Section: Introductionmentioning

confidence: 99%

Energy-optimal routes for electric vehicles

Baum

Dibbelt

Pajor

et al. 2013

Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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Abstract. We study the problem of electric vehicle route planning, where an important aspect is computing paths that minimize energy consumption. Thereby, any method must cope with specific properties, such as recuperation, battery constraints (over-and under-charging), and frequently changing cost functions (e. g., due to weather conditions). This work presents a practical algorithm that quickly computes energy-optimal routes for networks of continental scale. Exploiting multi-level overlay graphs [26,31], we extend the Customizable Route Planning approach [8] to our scenario in a sound manner. This includes the efficient computation of profile queries and the adaption of bidirectional search to battery constraints. Our experimental study uses detailed consumption data measured from a production vehicle (Peugeot iOn). It reveals for the network of Europe that a new cost function can be incorporated in about five seconds, after which we answer random queries within 0.3 ms on average. Additional evaluation on an artificial but realistic [22,36] vehicle model with unlimited range demonstrates the excellent scalability of our algorithm: Even for long-range queries across Europe it achieves query times below 5 ms on average-fast enough for interactive applications. Altogether, our algorithm exhibits faster query times than previous approaches, while improving (metric-dependent) preprocessing time by three orders of magnitude.

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Section: Introductionmentioning

confidence: 99%

Energy-optimal routes for electric vehicles

Baum

Dibbelt

Pajor

et al. 2013

Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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“…[Som12,LPS13]). In general, an overlay network G is a virtual network of nodes and logical links that is built on top of an underlying real network G; i.e., V (G ) ⊂ V (G) and an edge in G (a "virtual edge") corresponds to a path in G (see, e.g., [EFK + 12]).…”

Section: Algorithms On General Networkmentioning

confidence: 99%

Distributed approximation algorithms for weighted shortest paths

Nanongkai

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

139

257

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A distributed network is modeled by a graph having n nodes (processors) and diameter D. We study the time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O(log n) bandwidth restriction on edges (the standard synchronous CONGEST model). The question whether approximation algorithms help speed up the shortest paths (more precisely distance computation) was raised , which holds even when D = Θ(log n), up to a poly log n factor.As a by-product of our technique, we obtain a simpleÕ(n)-time (1 + o(1))-approximation algorithm for APSP, improving the previousÕ(n)-time O(1)-approximation algorithm following from the results of Lenzen and Patt-Shamir. We also prove a matching lower bound. Our techniques also yield anÕ(n 1/2 ) time algorithm on fully-connected networks, which guarantees an exact solution for SSSP and a (2 + o(1))-approximate solution for APSP. All our algorithms rely on two new simple tools: light-weight algorithm for bounded-hop SSSP and shortest-path diameter reduction via shortcuts. These tools might be of an independent interest and useful in designing other distributed algorithms.

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“…Given a query, algorithms first retrieve the shortest path and then concatenate them by the shortest paths not in index. The recent literature [20] gives a full overview of the works on the shortest path problem. Recently, there are several works on the shortest path problem in time-dependent graphs.…”

Section: Exp-4 Impact Of the Length Of Time Interval [T D Ta]mentioning

confidence: 99%

Finding the cost-optimal path with time constraint over time-dependent graphs

Yang

Gao

et al. 2014

Proc. VLDB Endow.

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Shortest path query is an important problem and has been well studied in static graphs. However, in practice, the costs of edges in graphs always change over time. We call such graphs as timedependent graphs. In this paper, we study how to find a costoptimal path with time constraint in time-dependent graphs. Most existing works regarding the Time-Dependent Shortest Path (TD-SP) problem focus on finding a shortest path with the minimum travel time. All these works are based on the following fact: the earliest arrival time at a vertex v can be derived from the earliest arrival time at v's neighbors. Unfortunately, this fact does not hold for our problem. In this paper, we propose a novel algorithm to compute a cost-optimal path with time constraint in time-dependent graphs. We show that the time and space complexities of our algorithm are O(kn log n + mk) and O((n + m)k) respectively. We confirm the effectiveness and efficiency of our algorithm through conducting experiments on real datasets with synthetic cost.

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Shortest-path queries in static networks

Cited by 194 publications

References 175 publications

Energy-optimal routes for electric vehicles

Energy-optimal routes for electric vehicles

Distributed approximation algorithms for weighted shortest paths

Finding the cost-optimal path with time constraint over time-dependent graphs

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