12,278 research outputs found

    Core Routing on Dynamic Time-Dependent Road Networks

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    Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-level hierarchical approach for pointto-point shortest paths computations to the time-dependent case. This method, also known as core routing in the literature for static graphs, consists in the selection of a small subnetwork where most of the computations can be carried out, thus reducing the search space. We combine this approach with bidirectional goal-directed search in order to obtain an algorithm capable of finding shortest paths in a matter of milliseconds on continental sized networks. Moreover, we tackle the dynamic scenario where the piecewise linear functions that we use to model time-dependent arc costs are not fixed, but can have their coefficients updated requiring only a small computational effort

    Finding the Shortest Path in Dynamic Network using Labeling Algorithm

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    Abstract This study concerns the problem of finding shortest paths from one node to all other nodes in networks for which arc costs can vary with time, each arc has a transit time and parking with a corresponding time-varying cost is allowed at the nodes. it show that this problem is equivalent to a classical shortest path problem in a timeexpanded network. The label correcting algorithm is used for finding shortest paths. Keywords: Dynamic shortest paths, time-expanded network, label correcting algorithm. Introduction In congested transportation networks, arc travel times change over time due to time-of-day variations in traffic congestion. Even if one can account for these time-of-day variations, future travel times can at best be known a priori with uncertainty due to unforeseen events, such as poor roadway conditions, vehicle breakdowns, traffic accidents, and driver behavior. In this work, we develop path search techniques that explicitly consider the inherent time-varying nature of future travel times. Recent studies have focused on time-dependent graphs Review of the shortest path proble

    Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind

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    We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs

    Route Planning in Transportation Networks

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    We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

    K shortest paths in stochastic time-dependent networks

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    A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs
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