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.

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U2 - 10.1111/j.1538-4632.1997.tb00966.x

DO - 10.1111/j.1538-4632.1997.tb00966.x

M3 - Article

AN - SCOPUS:0031430841

SN - 0016-7363

VL - 29

SP - 298

EP - 313

JO - Geographical Analysis

JF - Geographical Analysis

IS - 4

ER -