Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Computing strictly-second shortest paths
Information Processing Letters
SIAM Journal on Computing
Optimizing computations for effective block-processing
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Finding next-to-shortest paths in a graph
Information Processing Letters
Improved algorithm for finding next-to-shortest paths
Information Processing Letters
A simpler and more efficient algorithm for the next-to-shortest path problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Hi-index | 0.00 |
Given an edge-weighted undirected graph and two vertices s and t, the next-to-shortest path problem is to find an st-path whose length is minimum among all st-paths of lengths strictly larger than the shortest path length. The problem is shown to be polynomially solvable if all edge weights are positive, while the complexity status for the nonnegative weight case was open. In this paper we show that the problem in undirected graphs admits a polynomial-time algorithm even if all edge weights are nonnegative, solving the open problem. To solve the problem, we introduce a common generalization of the undirected graph version and the acyclic digraph version of the k vertex-disjoint paths problem.