Label-Setting Algorithm for Multi-Destination <i>K</i> Simple Shortest Paths Problem and Application

Abstract

The k shortest paths problem finds applications in multiple fields. Of particular interest in the transportation field is the variant of finding k simple shortest paths (KSSP), which has a higher complexity. This research presents a novel label-setting algorithm for the multi-destination KSSP problem in directed networks that obviates repeated applications of the algorithm to each destination (necessary in existing deviation-based algorithms), resulting in a significant computational speedup. It is shown that the proposed algorithm is exact and flexible enough to handle several variants of the problem by appropriately modifying the termination condition. Theoretically, it is also shown to be faster than state-of-the-art algorithms in sparse and dense networks whenever the number of labels created is sub-polynomial in network size. A heuristic method and optimized data structures are proposed to improve the algorithm’s scalability and worst-case performance. The computational results show that the proposed heuristic provides two to three orders of magnitude computational time speedups (29–1416 times across different networks) with negligible loss in solution quality (maximum average deviation of 0.167% from the optimal solution). Finally, a practical application of the proposed method is illustrated to determine the gravity of an edge (relative structural importance) in a network.

Keywords

• <i>k</i> simple shortest paths
• label-setting algorithm
• loopless paths
• network optimization
• edge importance
• edge ranking