Journal of Advanced Transportation

Qiang Meng
Der-Horng Lee
Ruey Long Cheu

This paper deals with an interesting problem about how to efficiently compute the number of different efficient paths between an origin-destination pair for a transportation network because these efficient paths are the possible paths used by drivers to some extent. Based on a novel triangle operation derived, it first presents a polynomial-time combinatorial algorithm that can obtain the number of different simple paths between any two nodes for an acyclic network as well as the total travel cost of these paths. This paper proceeds to develop a combinatorial algorithm with polynomial-time complexity for both counting the different efficient paths between an origin-destination pair and calculating the total travel cost of these paths. As for applications, this paper shows that the preceding two algorithms can yield the lower and upper bounds for the number of different simple paths between an origin-destination pair, while it has already be recognized that a polynomial-time algorithm getting such a number does not exist for a general network. Furthermore, the latter algorithm can be applied for developing a heuristic method for the traffic counting location problem arising from the origin-destination matrix estimation problems.