Dijkstra’s Algorithm On-Line: An Empirical Case Study from Public Railroad Transport

Schulz, Frank; Wagner, Dorothea; Weihe, Karsten

doi:10.1007/3-540-48318-7_11

Cited by 92 publications

(154 citation statements)

References 5 publications

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“…The first published practical approach to fast route planning [67,68] uses a set of nodes V 1 whose removal partitions the graph G = G 0 into small components. Now consider the overlay graph G 1 = (V 1 , E 1 ) where edges in E 1 are shortcuts corresponding to shortest paths in G that do not contain nodes from V 1 in their interior.…”

Section: Exploiting Hierarchymentioning

confidence: 99%

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Engineering Route Planning Algorithms

Delling

Sanders

Schultes

et al. 2009

Lecture Notes in Computer Science

Self Cite

362

235

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Abstract. Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra's algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.

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Section: Exploiting Hierarchymentioning

confidence: 99%

“…The first implementation had disappointing speedups (e.g. compared to [67]) and preprocessing times that would be prohibitive for large networks.…”

Section: Exploiting Hierarchymentioning

confidence: 99%

Engineering Route Planning Algorithms

Delling

Sanders

Schultes

et al. 2009

Lecture Notes in Computer Science

Self Cite

362

235

View full text Add to dashboard Cite

show abstract

“…All edges represented by straight-line segments 17,14] are graphs generated from the timetables. For the purpose of this paper, we assume that each station that any train stops at corresponds to a vertex, and an undirected edge is introduced for each pair of stations for which there is a nonstop service in either direction.…”

Section: Figmentioning

confidence: 99%

Fast Layout Methods for Timetable Graphs

et al. 2001

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Abstract.Timetable graphs are used to analyze transportation networks. In their visualization, vertex coordinates are fixed to preserve the underlying geography, but due to small angles and overlaps, not all edges should be represented by geodesics (straight lines or great circles). A previously introduced algorithm represents a subset of the edges by Bézier curves, and places control points of these curves using a forcedirected approach [5]. While the results are of very good quality, the running times make the approach impractical for interactive systems. In this paper, we present a fast layout algorithm using an entirely different approach to edge routing, based on directions of control segments rather than positions of control points. We reveal an interesting theoretical connection with Tutte's barycentric layout method [18], and our computational studies show that this new approach yields satisfactory layouts even for huge timetable graphs within seconds.

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“…During the last years, speed-up techniques have been developed for road networks (see [14,18] for an overview), that make the shortest path computation a matter of microseconds [4] even on huge road networks consisting of millions of nodes and edges. One core part of many of these speed-up techniques is the insertion of shortcuts [3,5,7,8,9,11,13,15,16,17], i.e. additional edges (u, v) whose length is the distance from u to v and that represent shortest u-v-paths in the graph.…”

Section: Introductionmentioning

confidence: 99%

“…Speed-up techniques that incorporate the usage of shortcuts are the following. Given a graph G = (V, E) the multi-level overlay graph technique [5,11,15,16,17] uses some centrality measures or separation strategies to choose a set of important nodes V on the graph and sets the shortcuts S such that the graph (V , S) is edge minimal among all graphs (V , E ) for which the distances between nodes in V are the same in (V, E) and (V , E ). Highway hierarchies [13] and reach based pruning [8,9] iteratively sparsificate the graph according to the importance of the nodes.…”

Section: Introductionmentioning

confidence: 99%

The Shortcut Problem – Complexity and Approximation

Bauer

D’Angelo

Delling

et al. 2009

Lecture Notes in Computer Science

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Abstract. During the last years, speed-up techniques for DIJKSTRA's algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent shortest paths in the graph. Until now, all existing shortcut-insertion strategies are heuristics and no theoretical results on the topic are known. In this work, we formalize the problem of adding shortcuts as a graph augmentation problem, study the algorithmic complexity of the problem, give approximation algorithms and show how to stochastically evaluate a given shortcut assignment on graphs that are too big to evaluate it exactly.

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Dijkstra’s Algorithm On-Line: An Empirical Case Study from Public Railroad Transport

Cited by 92 publications

References 5 publications

Engineering Route Planning Algorithms

Engineering Route Planning Algorithms

Fast Layout Methods for Timetable Graphs

The Shortcut Problem – Complexity and Approximation

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