On the exponent of the all pairs shortest path problem

The multiple pairs shortest path problem (MPSP) arises in many applications where the shortest paths and distances between only some specific pairs of origin-destination (OD) nodes in a network are desired. The traditional repeated single-source shortest ...

Given an arbitrary directed graph G=(V,E) with non-negative edge lengths, we present an algorithm that computes all pairs shortest paths in time O(mn+mlgn+nT(m,n)), where m is the number of different edges contained in shortest paths and T(m,n) is the ...

Uncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths. With help from the operational law of uncertainty theory, this paper gives the uncertainty distribution of the shortest path length. Also, ...