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Shortest Paths in Nearly Conservative Digraphs

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Parameterized and Exact Computation (IPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8894))

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Abstract

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.

Zoltán Király—Research was supported by grants (no. CNK 77780 and no.  K 109240) from the National Development Agency of Hungary, based on a source from the Research and Technology Innovation Fund.

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Acknowledgment

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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Authors and Affiliations

  1. Department of Computer Science and Egerváry Research Group (MTA-ELTE), Eötvös University, Pázmány Péter Sétány 1/C, Budapest, Hungary

    Zoltán Király

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  1. Zoltán Király
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Correspondence to Zoltán Király .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan

  2. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Király, Z. (2014). Shortest Paths in Nearly Conservative Digraphs. In: Cygan, M., Heggernes, P. (eds) Parameterized and Exact Computation. IPEC 2014. Lecture Notes in Computer Science(), vol 8894. Springer, Cham. https://doi.org/10.1007/978-3-319-13524-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-13524-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13523-6

  • Online ISBN: 978-3-319-13524-3

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