Shortest Paths in Nearly Conservative Digraphs

  • Zoltán KirályEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)


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


Conservative weights All Pairs Shortest Paths FPT algorithm Mixed graph 



The author is thankful to András Frank who asked a special case of this problem, and also to Dániel Marx who proposed the generalization to nearly conservative digraphs.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer Science and Egerváry Research Group (MTA-ELTE)Eötvös UniversityBudapestHungary

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