## A Comparative Study of k-Shortest Path Algorithms (1995)

Venue: | In Proc. of 11th UK Performance Engineering Workshop |

Citations: | 17 - 0 self |

### BibTeX

@INPROCEEDINGS{Brander95acomparative,

author = {A. W. Brander and M. C. Sinclair},

title = {A Comparative Study of k-Shortest Path Algorithms},

booktitle = {In Proc. of 11th UK Performance Engineering Workshop},

year = {1995},

pages = {370--379}

}

### OpenURL

### Abstract

Efficient management of networks requires that the shortest route from one point (node) to another is known; this is termed the shortest path. It is often necessary to be able to determine alternative routes through the network, in case any part of the shortest path is damaged or busy. The k-shortest paths represent an ordered list of the alternative routes available. Four algorithms were selected for more detailed study from over seventy papers written on this subject since the 1950's. These four were implemented in the `C' programming language and, on the basis of the results, an assessment was made of their relative performance. 1 The Background The shortest path through a network is the least cost route from a given node to another given node, and this path will usually be the preferred route between those two nodes. When the shortest path between two nodes is not available for some reason, it is necessary to determine the second shortest path. If this too is not available, a thir...

### Citations

33 |
An efficient algorithm for K shortest simple paths
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- 1982
(Show Context)
Citation Context ...shall concentrate on. 5 Literature Survey A literature survey was conducted to find previous work on KSPs, revealing some 70 papers from many different branches of modern mathematics. Four algorithms =-=[1, 2, 4, 5]-=- from among these were chosen for implementation and speed comparison. 6 Algorithm Selection The criteria for algorithm selection was based purely on the expected speed of operation of the algorithm i... |

27 |
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(Show Context)
Citation Context ...used extensively; and particular care was taken in the management of dynamic memory. 7.1 Yen The shortest path (containing psn nodes) is found using a standard shortestpath algorithm (e.g. Dijkstra's =-=[6]-=-) and placed in the results list (Yen's list A). Yen [1] takes every node in the shortest path, except the terminating node and calculates another shortest path (spur) from each selected node to the t... |

15 |
A method for the solution of the n-th best path problem
- Hoffman, Pavley
- 1959
(Show Context)
Citation Context ...shall concentrate on. 5 Literature Survey A literature survey was conducted to find previous work on KSPs, revealing some 70 papers from many different branches of modern mathematics. Four algorithms =-=[1, 2, 4, 5]-=- from among these were chosen for implementation and speed comparison. 6 Algorithm Selection The criteria for algorithm selection was based purely on the expected speed of operation of the algorithm i... |

11 |
TL, Orlin JB. Network Flows: theory, algorithms, and applications
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- 1993
(Show Context)
Citation Context ...sarily just concerned with the distance and therefore may not obey these rules. This is an important point when mentally visualising the expected operation of a KSP algorithm. The binary minimum heap =-=[3]-=- is a convenient method for storing data that is entered in a random order and output in an ordered fashion, and it is used here to store a record of the paths awaiting selection as the next shortest.... |

3 |
Finding the K Shortest Loopless Paths in a Network. Management Science
- JY
- 1971
(Show Context)
Citation Context ... computer science and transportation science. 2 The Problem The work presented here was driven by the desire to find a faster algorithm to calculate the KSPs between nodes in a network than that, Yen =-=[1]-=-, used to date by the second author. It was realised that Lawler [2] had investigated this problem and improved on Yen [1], and this raised the question of whether there were even faster methods. 3 De... |

2 |
A binary enumeration tree to find K shortest paths
- Carraresi, Sodini
- 1983
(Show Context)
Citation Context ...ompare them all without implementing them and as such, the following papers present alternative techniques from other fields that may yet perform faster than Hoffman's algorithm: Shier [8], Carraresi =-=[9]-=-, and Boffey [10]. However, these do not all meet the restrictions of loopless and nondisjoint paths, so extra precautions will have to be taken. 10 Acknowledgements The research that is described in ... |

1 | A procedure for computing the k best solutions to discrete optimisation problems and its application to the shortest path problem - EL - 1972 |

1 |
Mikac B. Ultra-high capacity optical transmission network: European research project COST 239
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- 1993
(Show Context)
Citation Context ...f overall best speed. This can only be achieved by comparing the run-times of the algorithms in tests on real networks. The results of one such series of runs on the COST 239 European Optical Network =-=[7]-=- are shown in Figure 3. This figure demonstrates a staggering improvement in the performance of the algorithms, between Katoh and Hoffman; and yet Katoh is the later, more complicated algorithm. The i... |

1 |
Iterative methods for determining the k shortest paths in a network. Networks
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- 1976
(Show Context)
Citation Context ... difficult to compare them all without implementing them and as such, the following papers present alternative techniques from other fields that may yet perform faster than Hoffman's algorithm: Shier =-=[8]-=-, Carraresi [9], and Boffey [10]. However, these do not all meet the restrictions of loopless and nondisjoint paths, so extra precautions will have to be taken. 10 Acknowledgements The research that i... |

1 |
The all-to-all alternative route problem. Operation Research -- Rairo-Recherche Operationelle
- Boffey
- 1993
(Show Context)
Citation Context ...without implementing them and as such, the following papers present alternative techniques from other fields that may yet perform faster than Hoffman's algorithm: Shier [8], Carraresi [9], and Boffey =-=[10]-=-. However, these do not all meet the restrictions of loopless and nondisjoint paths, so extra precautions will have to be taken. 10 Acknowledgements The research that is described in this paper was un... |