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arXiv · 1409.7033

Shortest Paths in Nearly Conservative Digraphs

Zoltán Király
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Abstract

We introduce the following notion: a digraph $D=(V,A)$ with arc weights $c: A\rightarrow \R$ 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.

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Zoltán Király. 2014-09-24. Shortest Paths in Nearly Conservative Digraphs. https://arxiv.org/abs/1409.7033

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