## Combining Speed-Up Techniques for Shortest-Path Computations (2004)

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Venue: | In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS |

Citations: | 21 - 6 self |

### BibTeX

@INPROCEEDINGS{Holzer04combiningspeed-up,

author = {Martin Holzer and Frank Schulz and Thomas Willhalm},

title = {Combining Speed-Up Techniques for Shortest-Path Computations},

booktitle = {In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS},

year = {2004},

pages = {269--284},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.

### Citations

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Citation Context ...e route planning systems for cars, bikes, and hikers [1,2] or scheduled vehicles like trains and buses [3,4], spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra =-=[7]-=-, with a worst-case running time of O(m + n log n) using Fibonacci heaps [8], there are many recent algorithms that solve variants and special cases of the shortest-path problem with better running ti... |

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Citation Context ... 269–284, 2004. c○ Springer-Verlag Berlin Heidelberg 2004s270 M. Holzer, F. Schulz, and T. Willhalm Goal-Directed Search modifies the given edge weights to favor edges leading towards the target n=-=ode [14,15]-=-. With graphs from timetable information, a speed-up in running time of a factor of roughly 1.5 is reported in [16]. Bi-Directed Search starts a second search backwards, from the target to the source ... |

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Citation Context ...5 · n edges, and each of these is replaced by two directed edges, one in either direction. Random Waxman Graphs. The construction of these graphs is based on a random graph model introduced by Waxman=-= [25]. -=-Input parameters are the number of nodes n and two positive rational numbers α and β. The nodes are again uniformly distributed in a square of a lateral length of 1, and the probability that an edge... |

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Citation Context ...1000 · i nodes (i =1,...,10).sCombining Speed-Up Techniques for Shortest-Path Computations 275 Random Planar Graphs. For the construction of random planar graphs, we used a generator provided by LEDA=-= [24]-=-. A given number of n nodes are uniformly distributed in a square with a lateral length of 1, and a triangulation of the nodes is computed. This yields a complete undirected planar graph. Finally, edg... |

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Citation Context ...cles like trains and buses [3,4], spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) using Fibonacci heaps =-=[8]-=-, there are many recent algorithms that solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see [9] for an experimental comparison, [10]... |

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Citation Context ...O(m + n log n) using Fibonacci heaps [8], there are many recent algorithms that solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see =-=[9] f-=-or an experimental comparison, [10] for a survey and some more recent work [11,12,13]). It is common practice to improve the running time of Dijkstra’s algorithm heuristically while correctness of t... |

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Citation Context ...ch modifies the given edge weights to favor edges leading towards the target node [14,15]. With graphs from timetable information, a speed-up in running time of a factor of roughly 1.5 is reported in =-=[16]-=-. Bi-Directed Search starts a second search backwards, from the target to the source (see [17], Section 4.5). Both searches stop when their search horizons meet. Experiments in [18] showed that the se... |

55 | Exact and Approximate Distances in Graphs – A Survey
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(Show Context)
Citation Context ... [8], there are many recent algorithms that solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see [9] for an experimental comparison, =-=[10] f-=-or a survey and some more recent work [11,12,13]). It is common practice to improve the running time of Dijkstra’s algorithm heuristically while correctness of the solution is still provable, i.e., ... |

54 | An extremely fast, exact algorithm for finding shortest paths in static networks with geographical background - Lauther - 2004 |

53 | Geometric speed-up techniques for finding shortest paths in large sparse graphs
- Wagner, Willhalm
- 2003
(Show Context)
Citation Context ...respected in the search. More precisely, the bounding box of all nodes that can be reached on a shortest path using this edge is given. Speed-up factors in the range between 10 and 20 can be achieved =-=[23]-=-. Goal-directed search and shortest-path bounding boxes are only applicable if a layout of the graph is provided. Multi-level approach and shortest-path bounding boxes both require a preprocessing, ca... |

53 | Reach-based routing: A new approach to shortest path algorithms optimized for road networks - Gutman - 2004 |

43 |
Path Computation Algorithms for Advanced Traveler Information System
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Citation Context ... 269–284, 2004. c○ Springer-Verlag Berlin Heidelberg 2004s270 M. Holzer, F. Schulz, and T. Willhalm Goal-Directed Search modifies the given edge weights to favor edges leading towards the target n=-=ode [14,15]-=-. With graphs from timetable information, a speed-up in running time of a factor of roughly 1.5 is reported in [16]. Bi-Directed Search starts a second search backwards, from the target to the source ... |

38 |
An Efficient Path Computation Model for Hierarchically Structured Topographical Road Maps
- Jung, Pramanik
- 2002
(Show Context)
Citation Context ...echnique, speed-up factors of more than 3.5 have been observed for road map and public transport graphs [20]. Timetable information queries could be improved by a factor of 11 (see [21]), and also in =-=[22]-=- good improvements for road maps are reported. Shortest-Path Bounding Boxes provide a necessary condition for each edge, if it has to be respected in the search. More precisely, the bounding box of al... |

34 | A simple shortest path algorithm with linear average time, in
- Goldberg
(Show Context)
Citation Context ...solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see [9] for an experimental comparison, [10] for a survey and some more recent work =-=[11,12,13]).-=- It is common practice to improve the running time of Dijkstra’s algorithm heuristically while correctness of the solution is still provable, i.e., it is guaranteed that a shortest path is returned ... |

32 | Bidirectional heuristic search reconsidered
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- 1997
(Show Context)
Citation Context ...ds, from the target to the source (see [17], Section 4.5). Both searches stop when their search horizons meet. Experiments in [18] showed that the search space can be reduced by a factor of 2, and in =-=[19]-=- it was shown that combinations with the goal-directed search can be beneficial. Multi-Level Approach takes advantage of hierarchical coarsenings of the given graph, where additional edges have to be ... |

28 | Materialization trade-offs in hierarchical shortest path algorithms, in:Symposium on Large Spatial Databases
- Shekhar, Fetterer, et al.
- 1997
(Show Context)
Citation Context ...ths in large, sparse graphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers [1,2] or scheduled vehicles like trains and buses [3,4], spatial databases =-=[5]-=-, and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) using Fibonacci heaps [8], there are many recent algorithms that solve varian... |

28 | Single-source shortest-paths on arbitrary directed graphs in linear average-case time
- Meyer
- 2001
(Show Context)
Citation Context ...solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see [9] for an experimental comparison, [10] for a survey and some more recent work =-=[11,12,13]).-=- It is common practice to improve the running time of Dijkstra’s algorithm heuristically while correctness of the solution is still provable, i.e., it is guaranteed that a shortest path is returned ... |

26 | Using multi-level graphs for timetable information in railway systems
- Schulz, Wagner, et al.
- 2002
(Show Context)
Citation Context ... path. Using this technique, speed-up factors of more than 3.5 have been observed for road map and public transport graphs [20]. Timetable information queries could be improved by a factor of 11 (see =-=[21]-=-), and also in [22] good improvements for road maps are reported. Shortest-Path Bounding Boxes provide a necessary condition for each edge, if it has to be respected in the search. More precisely, the... |

22 | Engineering multi-level overlay graphs for shortest-path queries - Holzer, Schulz, et al. - 2006 |

21 |
Time depending shortest-path problems with applications to railway networks
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(Show Context)
Citation Context ...single-target shortest paths in large, sparse graphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers [1,2] or scheduled vehicles like trains and buses =-=[3,4]-=-, spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) using Fibonacci heaps [8], there are many recent algor... |

21 | M.V.: Formal-Language-Constrained Path Problems
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- 2000
(Show Context)
Citation Context ...aphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers [1,2] or scheduled vehicles like trains and buses [3,4], spatial databases [5], and web searching =-=[6]-=-. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) using Fibonacci heaps [8], there are many recent algorithms that solve variants and special cases of... |

20 | Shortest path algorithms: Engineering aspects, in - Goldberg |

18 |
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- 1969
(Show Context)
Citation Context ...1.5 is reported in [16]. Bi-Directed Search starts a second search backwards, from the target to the source (see [17], Section 4.5). Both searches stop when their search horizons meet. Experiments in =-=[18]-=- showed that the search space can be reduced by a factor of 2, and in [19] it was shown that combinations with the goal-directed search can be beneficial. Multi-Level Approach takes advantage of hiera... |

16 | Classical and contemporary shortest path problems in road networks: Implementation and experimental analysis of the TRANSIMS router
- BARRETT, BISSET, et al.
- 2002
(Show Context)
Citation Context ...e problem of (repetitively) finding single-source single-target shortest paths in large, sparse graphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers =-=[1,2]-=- or scheduled vehicles like trains and buses [3,4], spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) usin... |

13 |
A comparison between label-setting and label-correcting algorithms for computing one-to-one shortest paths
- Zahn, Noon
(Show Context)
Citation Context ...e problem of (repetitively) finding single-source single-target shortest paths in large, sparse graphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers =-=[1,2]-=- or scheduled vehicles like trains and buses [3,4], spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) usin... |

12 |
An integrated traffic information system
- Preuss, Syrbe
- 1997
(Show Context)
Citation Context ...single-target shortest paths in large, sparse graphs. Typical applications of this problem include route planning systems for cars, bikes, and hikers [1,2] or scheduled vehicles like trains and buses =-=[3,4]-=-, spatial databases [5], and web searching [6]. Besides the classical algorithm by Dijkstra [7], with a worst-case running time of O(m + n log n) using Fibonacci heaps [8], there are many recent algor... |

12 | Experimental evaluation of a new shortest path algorithm
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- 2002
(Show Context)
Citation Context ...solve variants and special cases of the shortest-path problem with better running time (worst-case or average-case; see [9] for an experimental comparison, [10] for a survey and some more recent work =-=[11,12,13]).-=- It is common practice to improve the running time of Dijkstra’s algorithm heuristically while correctness of the solution is still provable, i.e., it is guaranteed that a shortest path is returned ... |

10 | Engineering Shortest Paths and Layout Algorithms for Large Graphs - Willhalm - 2005 |

7 | Route Planning Algorithms for Car Navigation - Flinsenberg - 2004 |

4 |
Hierarchical speed-‐up techniques for shortest-‐path algorithms
- Holzer
- 2003
(Show Context)
Citation Context ... only a small fraction of these edges has to be considered to find a shortest path. Using this technique, speed-up factors of more than 3.5 have been observed for road map and public transport graphs =-=[20]-=-. Timetable information queries could be improved by a factor of 11 (see [21]), and also in [22] good improvements for road maps are reported. Shortest-Path Bounding Boxes provide a necessary conditio... |

3 | Acceleration of shortest path computation - Köhler, Möhring, et al. - 2004 |

2 | Shortest path speedup techniques - Willhalm, Wagner - 2006 |