### Abstract

In real-world applications, the k-shortest-paths between a pair of nodes on a network will often be slight variations of one another. This could be a problem for many path-based models, particularly those on capacitated networks where different routing alternatives are needed that are less likely to encounter the same capacity constraints. This paper develops a method to solve for k differentiated paths that are relatively short and yet relatively different from one another but not necessarily disjoint. Our method utilizes the sum of a path's distance plus some fraction of its shared distance with each other path. A minimax algorithm is used to select the path whose largest sum of length, plus shared length vis-à-vis each previously selected path, is as small as possible. We present computational results for the Chinese railway system, comparing the paths generated by a standard k-shortest-path algorithm with those from our new model.

Original language | English (US) |
---|---|

Pages (from-to) | 298-313 |

Number of pages | 16 |

Journal | Geographical Analysis |

Volume | 29 |

Issue number | 4 |

State | Published - Oct 1997 |

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### ASJC Scopus subject areas

- Geography, Planning and Development

### Cite this

*Geographical Analysis*,

*29*(4), 298-313.

**A minimax method for finding the k best "differentiated" paths.** / Kuby, Michael; Zhongyi, Xu; Xiaodong, Xie.

Research output: Contribution to journal › Article

*Geographical Analysis*, vol. 29, no. 4, pp. 298-313.

}

TY - JOUR

T1 - A minimax method for finding the k best "differentiated" paths

AU - Kuby, Michael

AU - Zhongyi, Xu

AU - Xiaodong, Xie

PY - 1997/10

Y1 - 1997/10

N2 - In real-world applications, the k-shortest-paths between a pair of nodes on a network will often be slight variations of one another. This could be a problem for many path-based models, particularly those on capacitated networks where different routing alternatives are needed that are less likely to encounter the same capacity constraints. This paper develops a method to solve for k differentiated paths that are relatively short and yet relatively different from one another but not necessarily disjoint. Our method utilizes the sum of a path's distance plus some fraction of its shared distance with each other path. A minimax algorithm is used to select the path whose largest sum of length, plus shared length vis-à-vis each previously selected path, is as small as possible. We present computational results for the Chinese railway system, comparing the paths generated by a standard k-shortest-path algorithm with those from our new model.

AB - In real-world applications, the k-shortest-paths between a pair of nodes on a network will often be slight variations of one another. This could be a problem for many path-based models, particularly those on capacitated networks where different routing alternatives are needed that are less likely to encounter the same capacity constraints. This paper develops a method to solve for k differentiated paths that are relatively short and yet relatively different from one another but not necessarily disjoint. Our method utilizes the sum of a path's distance plus some fraction of its shared distance with each other path. A minimax algorithm is used to select the path whose largest sum of length, plus shared length vis-à-vis each previously selected path, is as small as possible. We present computational results for the Chinese railway system, comparing the paths generated by a standard k-shortest-path algorithm with those from our new model.

UR - http://www.scopus.com/inward/record.url?scp=0031430841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031430841&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031430841

VL - 29

SP - 298

EP - 313

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

IS - 4

ER -