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International Conference on Combinatorial Optimization and Applications

COCOA 2016: Combinatorial Optimization and Applications pp 113–127Cite as

Finding Disjoint Paths on Edge-Colored Graphs: A Multivariate Complexity Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10043))

Abstract

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate how the complexity of the problem depends on graph parameters (distance from disjoint paths and size of vertex cover), and that is not FPT-approximable. Moreover, we introduce a new variant of the problem, called MaxCDDP, whose goal is to find the maximum number of vertex-disjoint and color-disjoint uni-color paths. We extend some of the results of MaxCDP to this new variant, and we prove that unlike MaxCDP, MaxCDDP is already hard on graphs at distance two from disjoint paths.

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Notes

  1. 1.

    A graph is cubic when each of its vertices has degree 3.

  2. 2.

    Notice that, since \(|X| \leqslant d\), X can be computed in time \(O(n^d)\).

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Author information

Authors and Affiliations

  1. Dipartimento di Lettere e Comunicazione, Università degli Studi di Bergamo, Bergamo, Italy

    Riccardo Dondi

  2. Université Paris-Dauphine, PSL Research University, CNRS, LAMSADE, Paris, France

    Florian Sikora

Authors
  1. Riccardo Dondi
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  2. Florian Sikora
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Corresponding author

Correspondence to Florian Sikora .

Editor information

Editors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T-H. Hubert Chan

  2. City University of Hong Kong, Hong Kong, China

    Minming Li

  3. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

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© 2016 Springer International Publishing AG

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Dondi, R., Sikora, F. (2016). Finding Disjoint Paths on Edge-Colored Graphs: A Multivariate Complexity Analysis. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-48749-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48748-9

  • Online ISBN: 978-3-319-48749-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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