Shortest Paths in Nearly Conservative Digraphs
Data Structures and Algorithms
2014-09-26 v1 Combinatorics
Abstract
We introduce the following notion: a digraph with arc weights is called nearly conservative if every negative cycle consists of two arcs. Computing shortest paths in nearly conservative digraphs is NP-hard, and even deciding whether a digraph is nearly conservative is coNP-complete. We show that the "All Pairs Shortest Path" problem is fixed parameter tractable with various parameters for nearly conservative digraphs. The results also apply for the special case of conservative mixed graphs.
Cite
@article{arxiv.1409.7033,
title = {Shortest Paths in Nearly Conservative Digraphs},
author = {Zoltán Király},
journal= {arXiv preprint arXiv:1409.7033},
year = {2014}
}