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The Path Set Packing Problem

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Computing and Combinatorics (COCOON 2018)

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Abstract

In this paper, we study a variant of set packing, in which a set P of paths in a graph \(G=(V,E)\) is given, the goal is to find a maximum number of edge-disjoint paths of P. We show that the problem is NP-hard even if each path in P contains at most three edges, while it is hard to approximate within \(O(|E|^{1/2-\epsilon })\) for the general case unless \(NP=ZPP\). In the positive aspect, a parameterized algorithm relying on the maximum degree and the tree-width of G is derived. For tree networks, we present a polynomial time optimal algorithm.

This work was partially supported by NSFC Grant 11531014.

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Correspondence to Guochuan Zhang .

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Xu, C., Zhang, G. (2018). The Path Set Packing Problem. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_26

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94775-4

  • Online ISBN: 978-3-319-94776-1

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