1 research outputs found
A simpler and more efficient algorithm for the next-to-shortest path problem
Given an undirected graph with positive edge lengths and two
vertices and , the next-to-shortest path problem is to find an -path
which length is minimum amongst all -paths strictly longer than the
shortest path length. In this paper we show that the problem can be solved in
linear time if the distances from and to all other vertices are given.
Particularly our new algorithm runs in time for general
graphs, which improves the previous result of time for sparse
graphs, and takes only linear time for unweighted graphs, planar graphs, and
graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201