Improving Space Efficiency With Path Length Prediction for Finding $k$ Shortest Simple Paths

Abstract

Finding ${\mbi {k}}$ shortest simple paths in a directed graph is a fundamental problem in many engineering applications. Most existing algorithms such as Yen’s algorithm and its variants have polynomial worst-case time complexity, but their average-case running time is very high. The heuristic algorithm MPS can run significantly faster in practice. However, it requires an excessive amount of memory space. In this paper, we provide a new heuristic algorithm that achieves high space efficiency while maintaining similar average-case running time. We first propose a sidetrack representation of path, with which a path can be stored in ${\mbi {O}}{\bf (1)}$ space. We then show how to categorize a candidate path as either partial or complete, and restrict the number of paths added to the queue. In addition, we provide an empirical equation that can very accurately predict the ${\mbi {k}}$ th shortest path length, provided that a much smaller number of shortest paths have been found. Extensive experiments prove that our algorithm can achieve an ${\mbi {O(n)}}$ speedup in practice over Yen’s algorithm. In comparison with MPS, it runs up to three times faster and uses less space by an order of magnitude.