Michael Kuby is associate professor of geography, Arizona State University.
A Minimax Method for Finding the k Best “Differentiated” Paths
Article first published online: 3 SEP 2010
1997 The Ohio State University
Volume 29, Issue 4, pages 298–313, October 1997
How to Cite
Kuby, M., Zhongyi, X. and Xiaodong, X. (1997), A Minimax Method for Finding the k Best “Differentiated” Paths. Geographical Analysis, 29: 298–313. doi: 10.1111/j.1538-4632.1997.tb00966.x
- Issue published online: 3 SEP 2010
- Article first published online: 3 SEP 2010
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.