## Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study (2000)

Venue: | In Proc. Workshop on Algorithm Engineering |

Citations: | 11 - 2 self |

### BibTeX

@INPROCEEDINGS{Demetrescu00maintainingshortest,

author = {Camil Demetrescu and Daniele Frigioni and Alberto Marchetti-spaccamela and Umberto Nanni},

title = {Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study},

booktitle = {In Proc. Workshop on Algorithm Engineering},

year = {2000},

pages = {218--229}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present the first experimental study of the fully dynamic single-source shortest paths problem in digraphs with arbitrary (negative and non-negative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worst-case bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets. 1

### Citations

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Citation Context ...rk optimization, document formatting, routing in communication systems, robotics. For a comprehensive review of the application settings for the static and dynamic shortest paths problem, we refer to =-=[1]-=- and [15], respectively. Several theoretical results have been provided in the literature for the dynamic maintenance of shortest paths in graphs with positive arc weights (see, ? Partially supported ... |

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Citation Context ...ber of nodes considered by the algorithm and maintaining both the distance and the parent in the shortest paths tree. The common idea behind these algorithms is to use a technique of Edmonds and Karp =-=[6]-=-, which allows it to transform the weight of each arc in a digraph into a non-negative real without changing the shortest paths, and to apply an adaptation of Dijkstra's algorithm to the modified grap... |

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Citation Context ...s on algorithms and their implementation and practical evaluation. Many papers have been proposed in this field concerning the practical performances of static algorithms for shortest paths (see e.g. =-=[4, 5, 13]-=-), but very little is known for the experimental evaluation of dynamic shortest paths algorithms: [8] considers the fully dynamic single source shortest paths problem in digraphs with positive real ar... |

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Citation Context ...ithm of Frigioni et al. yield better results for specific kinds of test sets, e.g., where the range of values of arc weights is small. Our implementations were written in C++ with the support of LEDA =-=[14]-=-. The experimental platform including codes, test sets generators and results can be accessed over the Internet at the URL: ftp://www.dis.uniroma1.it/pub/demetres/experim/dsplib-1.1/ and was designed ... |

52 | On the computational complexity of dynamic graph problems. TCS
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Citation Context ...terature for the dynamic maintenance of shortest paths in graphs with positive arc weights (see, ? Partially supported by the IST Programme of the EU under contract n. IST-199914186 (ALCOM-FT). e.g., =-=[7, 9, 15, 16]-=-). We are aware of few efficient fully dynamic solutions for updating shortest paths in general digraphs with arbitrary (positive and non-positive) arc weights [10, 16]. Recently, an equally important... |

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Citation Context ...terature for the dynamic maintenance of shortest paths in graphs with positive arc weights (see, ? Partially supported by the IST Programme of the EU under contract n. IST-199914186 (ALCOM-FT). e.g., =-=[7, 9, 15, 16]-=-). We are aware of few efficient fully dynamic solutions for updating shortest paths in general digraphs with arbitrary (positive and non-positive) arc weights [10, 16]. Recently, an equally important... |

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Citation Context ...s on algorithms and their implementation and practical evaluation. Many papers have been proposed in this field concerning the practical performances of static algorithms for shortest paths (see e.g. =-=[4, 5, 13]-=-), but very little is known for the experimental evaluation of dynamic shortest paths algorithms: [8] considers the fully dynamic single source shortest paths problem in digraphs with positive real ar... |

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Citation Context ...ization, document formatting, routing in communication systems, robotics. For a comprehensive review of the application settings for the static and dynamic shortest paths problem, we refer to [1] and =-=[15]-=-, respectively. Several theoretical results have been provided in the literature for the dynamic maintenance of shortest paths in graphs with positive arc weights (see, ? Partially supported by the IS... |

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Citation Context ... We are not aware of any experimental study in the case of arbitrary arc weights. On the other hand, several papers report on experimental works concerning different dynamic graph problems (see e.g., =-=[2, 3, 11]-=-). In this paper we make a step toward this direction and we present the first experimental study of the fully dynamic single-source shortest paths problem in digraphs with arbitrary (negative and non... |

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Citation Context ...s on algorithms and their implementation and practical evaluation. Many papers have been proposed in this field concerning the practical performances of static algorithms for shortest paths (see e.g. =-=[4, 5, 13]-=-), but very little is known for the experimental evaluation of dynamic shortest paths algorithms: [8] considers the fully dynamic single source shortest paths problem in digraphs with positive real ar... |

17 | Fully dynamic shortest paths and negative cycles detection on digraphs with arbitrary arc weights
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Citation Context ...9914186 (ALCOM-FT). e.g., [7, 9, 15, 16]). We are aware of few efficient fully dynamic solutions for updating shortest paths in general digraphs with arbitrary (positive and non-positive) arc weights =-=[10, 16]-=-. Recently, an equally important research effort has been done in the field of algorithm engineering, aiming at bridging the gap between theoretical results on algorithms and their implementation and ... |

15 | Experimental analysis of dynamic minimum spanning tree algorithms
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Citation Context ... We are not aware of any experimental study in the case of arbitrary arc weights. On the other hand, several papers report on experimental works concerning different dynamic graph problems (see e.g., =-=[2, 3, 11]-=-). In this paper we make a step toward this direction and we present the first experimental study of the fully dynamic single-source shortest paths problem in digraphs with arbitrary (negative and non... |

14 | Semi-dynamic shortest paths and breadth-first search in digraphs
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Citation Context ...terature for the dynamic maintenance of shortest paths in graphs with positive arc weights (see, ? Partially supported by the IST Programme of the EU under contract n. IST-199914186 (ALCOM-FT). e.g., =-=[7, 9, 15, 16]-=-). We are aware of few efficient fully dynamic solutions for updating shortest paths in general digraphs with arbitrary (positive and non-positive) arc weights [10, 16]. Recently, an equally important... |

6 | An experimental study of dynamic algorithms for directed graphs - Frigioni, Miller, et al. - 1998 |

6 |
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Citation Context ... [5]; remaining arcs are then added by uniformly and independently selecting pairs of nodes in the graph. To avoid introducing negative and zero length cycles we use the potential method described in =-=[12]-=-. -- gen graph z(n,m,s,min,max): similar to gen graph, but all cycles in the generated graphs have exactly length zero. -- gen seq(G,q,min,max): issues a mixed sequence of q increase and decrease oper... |

3 |
Analysis of dynamic algorithms for the single source shortest path problem
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Citation Context ...eld concerning the practical performances of static algorithms for shortest paths (see e.g. [4, 5, 13]), but very little is known for the experimental evaluation of dynamic shortest paths algorithms: =-=[8]-=- considers the fully dynamic single source shortest paths problem in digraphs with positive real arc weights. We are not aware of any experimental study in the case of arbitrary arc weights. On the ot... |