## Speeding Up Dynamic Shortest Path Algorithms (2003)

### Cached

### Download Links

Venue: | INFORMS Journal on Computing, submitted |

Citations: | 14 - 5 self |

### BibTeX

@INPROCEEDINGS{Buriol03speedingup,

author = {L. S. Buriol and M. G. C. Resende and M. Thorup},

title = {Speeding Up Dynamic Shortest Path Algorithms},

booktitle = {INFORMS Journal on Computing, submitted},

year = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

Dynamic shortest path algorithms update the shortest paths to take into account a change in an edge weight. This paper describes a new technique that allows the reduction of heap sizes used by several dynamic shortest path algorithms. For unit weight change, the updates can be done without heaps. These reductions almost always reduce the computational times for these algorithms. In computational testing, several dynamic shortest path algorithms with and without the heap-reduction technique are compared. Speedups of up to a factor of 1.8 were observed using the heap-reduction technique on random weight changes and of over a factor of five on unit weight changes. We compare as well with Dijkstra 's algorithm, which recomputes the paths from scratch. With respect to Dijkstra's algorithm, speedups of up to five orders of magnitude are observed. 1.

### Citations

148 | Shorthest paths algorithms: Theory and experimental evaluation
- Cherkassky, Goldberg, et al.
- 1996
(Show Context)
Citation Context ...nstances from groupatt have 17 destinations nodes, while instances from subclasseshier,rand andwas have |V | destination nodes. The other eight classes are taken from Cherkassky, Goldberg, and Radzik =-=[2]-=-. They are Grid-SSquare-S,Grid-SWide,Grid-SLong,Grid-PHard,Rand-4,Rand-1:4,Rand-Len, and Acyc-Pos. They constitute all of the instances in [2] that only have non-negative arc lengths. The problem gene... |

119 | An incremental algorithm for a generalization of the shortest-path problem
- Ramalingam, Reps
- 1996
(Show Context)
Citation Context ...ted, and semi-dynamic incremental (decremental) if only increment (decrement) of weights is supported. Many algorithms were proposed for solving this problem, but the algorithm of Ramalingam and Reps =-=[20]-=- (RR), seems to be the most used [1, 10, 13]. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Co... |

91 | A genetic algorithm for the weight setting problem
- Ericsson, Resende, et al.
- 2001
(Show Context)
Citation Context ...cremental) if only increment (decrement) of weights is supported. Many algorithms were proposed for solving this problem, but the algorithm of Ramalingam and Reps [20] (RR), seems to be the most used =-=[1, 10, 13]-=-. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Considering semi-dynamic decremental algorithm... |

75 | Increasing internet capacity using local search
- Fortz, Thorup
- 2000
(Show Context)
Citation Context ...cremental) if only increment (decrement) of weights is supported. Many algorithms were proposed for solving this problem, but the algorithm of Ramalingam and Reps [20] (RR), seems to be the most used =-=[1, 10, 13]-=-. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Considering semi-dynamic decremental algorithm... |

69 | A new approach to dynamic all pairs shortest paths. Journal of the Association for Computing Machinery (JACM), 51(6):968–992 C. Demetrescu and
- Demetrescu, Italiano
- 2004
(Show Context)
Citation Context ...etrescu [3] usually has better performance. For maintaining all pairs shortest paths in directed graphs with real-valued edge weights, we refer the fully dynamic algorithms of Demetrescu and Italiano =-=[6, 7]-=- and the experimental results in Demetrescu, Emiliozzi, and Italiano [4]. In this paper, we show that the Ramalingam and Reps algorithm is not the best algorithm for all applications. However, one of ... |

53 | On the computational complexity of dynamic graph problems,” Theoret - Ramalingam, Reps - 1996 |

51 |
Fully dynamic algorithms for maintaining shortest paths trees
- Frigioni, Marchetti-Spaccamela, et al.
(Show Context)
Citation Context ... for updating a shortest path tree. Algorithm T RR − is a specialization of the Ramalingam and Reps algorithm (GRR − ) restricted to updating a shortest path tree. A similar algorithm was proposed=-= in [14]. Algo-=-rithm T RR − is described in Figure 14. Let arc a = ( −→ u,v) be the arc whose weight is decreased. In case the distance of node u does not change, the algorithm stops (line 1). Otherwise, du an... |

36 | F.: Fully dynamic all pairs shortest paths with real edge weights
- Demetrescu, Italiano
- 2006
(Show Context)
Citation Context ...etrescu [3] usually has better performance. For maintaining all pairs shortest paths in directed graphs with real-valued edge weights, we refer the fully dynamic algorithms of Demetrescu and Italiano =-=[6, 7]-=- and the experimental results in Demetrescu, Emiliozzi, and Italiano [4]. In this paper, we show that the Ramalingam and Reps algorithm is not the best algorithm for all applications. However, one of ... |

35 | Experimental analysis of dynamic all pairs shortest path algorithms
- Demetrescu, Italiano
(Show Context)
Citation Context ...est paths in directed graphs with real-valued edge weights, we refer the fully dynamic algorithms of Demetrescu and Italiano [6, 7] and the experimental results in Demetrescu, Emiliozzi, and Italiano =-=[4]-=-. In this paper, we show that the Ramalingam and Reps algorithm is not the best algorithm for all applications. However, one of its main advantages is having good performance in most situations. First... |

29 |
An on-line edge-deletion problem
- Shiloach, Even
- 1981
(Show Context)
Citation Context ... and Dionne [8]. Considering semi-dynamic decremental algorithms, previous work was done by Gallo [16] and Fujishige [15], while for the incremental case (arc deletion), we refer to Even and Shiloach =-=[9]-=-. Recently, Demetrescu, Frigioni, and Nanni [5] proposed a specialization of the Ramalingam and Reps algorithm for updating a shortest path tree, which is a revision of their previous work [13]. In th... |

26 | Fully dynamic output bounded single source shortest path problem
- Frigioni, Marchetti-Spaccamela, et al.
- 1996
(Show Context)
Citation Context ...nodes have no alternative shortest paths, but its performance can be poor otherwise. Again, RR has good performance in both situations. Even the algorithm of Frigioni, Marchetti-Spaccamela, and Nanni =-=[12]-=-, that theoretically is better than RR, was usually outperformed by RR in computational testing [12]. Many theoretical studies of dynamic shortest path algorithms have been carried out, but few experi... |

23 | Experimental analysis of dynamic algorithms for the single source shortest paths problem
- Frigioni, Lo®reda, et al.
- 1998
(Show Context)
Citation Context ...s usually outperformed by RR in computational testing [12]. Many theoretical studies of dynamic shortest path algorithms have been carried out, but few experimental results are known. Frigioni et al. =-=[11]-=- compared the algorithm of Ramalingam and Reps with the algorithm of Frigioni et al. [12], to update a single-source shortest path graph. They concluded that the algorithm of Ramalingam and Reps is us... |

22 | Semidynamic algorithms for maintaining single-source shortest path trees. Algorithmica
- Frigioni, Marchetti-Spaccamela, et al.
- 1998
(Show Context)
Citation Context ...cremental) if only increment (decrement) of weights is supported. Many algorithms were proposed for solving this problem, but the algorithm of Ramalingam and Reps [20] (RR), seems to be the most used =-=[1, 10, 13]-=-. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Considering semi-dynamic decremental algorithm... |

16 |
A space saving trick for directed dynamic transitive closure and shortest path algorithms
- King, Thorup
- 2001
(Show Context)
Citation Context ...OL, M.G.C. RESENDE, AND M. THORUP in the earlier paper, a semi-dynamic incremental algorithm was proposed. Their specialized algorithm did not make use of the special tree proposed by King and Thorup =-=[18]-=-. In graphs where only a few affected nodes have alternative shortest paths, the incremental algorithm proposed by Demetrescu [3] usually has better performance. For maintaining all pairs shortest pat... |

12 | Maintaining shortest paths in digraphs with arbitrary arc weights: An experimental study
- Demetrescu, Frigioni, et al.
- 2000
(Show Context)
Citation Context ...mental algorithms, previous work was done by Gallo [16] and Fujishige [15], while for the incremental case (arc deletion), we refer to Even and Shiloach [9]. Recently, Demetrescu, Frigioni, and Nanni =-=[5]-=- proposed a specialization of the Ramalingam and Reps algorithm for updating a shortest path tree, which is a revision of their previous work [13]. In the new version, they propose a fully dynamic alg... |

10 |
A new shortest path updating algorithm
- Goto, Sangiovanni-Vincentelli
- 1978
(Show Context)
Citation Context ...amalingam and Reps [20] (RR), seems to be the most used [1, 10, 13]. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli =-=[17]-=- and Dionne [8]. Considering semi-dynamic decremental algorithms, previous work was done by Gallo [16] and Fujishige [15], while for the incremental case (arc deletion), we refer to Even and Shiloach ... |

9 |
Étude et extension d’un algorithme de Murchland. Infor
- Dionne
- 1978
(Show Context)
Citation Context ...ps [20] (RR), seems to be the most used [1, 10, 13]. As previous work on algorithms for the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne =-=[8]-=-. Considering semi-dynamic decremental algorithms, previous work was done by Gallo [16] and Fujishige [15], while for the incremental case (arc deletion), we refer to Even and Shiloach [9]. Recently, ... |

9 |
Reoptimization procedures in shortest path problems. Rivista di Mathematica per le Scienze Economiche e Sociali 3
- Gallo
- 1980
(Show Context)
Citation Context ...r the dynamic shortest path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Considering semi-dynamic decremental algorithms, previous work was done by Gallo =-=[16]-=- and Fujishige [15], while for the incremental case (arc deletion), we refer to Even and Shiloach [9]. Recently, Demetrescu, Frigioni, and Nanni [5] proposed a specialization of the Ramalingam and Rep... |

9 | A Fixed Method for All Shortest Distances in a Directed Graph and for the Inverse Problem - Murchland - 1970 |

8 | Fully dynamic algorithms for path problems on directed graphs
- Demetrescu
- 2001
(Show Context)
Citation Context ...ithm did not make use of the special tree proposed by King and Thorup [18]. In graphs where only a few affected nodes have alternative shortest paths, the incremental algorithm proposed by Demetrescu =-=[3]-=- usually has better performance. For maintaining all pairs shortest paths in directed graphs with real-valued edge weights, we refer the fully dynamic algorithms of Demetrescu and Italiano [6, 7] and ... |

8 |
A note on the problem of updating shortest paths
- Fujishige
- 1981
(Show Context)
Citation Context ...est path problem, we refer to Murchland [19], Goto and Sangiovanni-Vincentelli [17] and Dionne [8]. Considering semi-dynamic decremental algorithms, previous work was done by Gallo [16] and Fujishige =-=[15]-=-, while for the incremental case (arc deletion), we refer to Even and Shiloach [9]. Recently, Demetrescu, Frigioni, and Nanni [5] proposed a specialization of the Ramalingam and Reps algorithm for upd... |