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Linear Algorithms for Red and Blue Domination in Convex Bipartite Graphs

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Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

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Abstract

In the k red (blue) domination problem for a bipartite graph \(G=(X,Y,E)\), we seek a subset \(D \subseteq X\) (respectively \(D \subseteq Y\)) of cardinality at most k that dominates vertices of Y (respectively X). The decision version of this problem is \(\textsc {NP}\)-complete for perfect elimination bipartite graphs but solvable in polynomial time for chordal bipartite graphs. We present a linear time algorithm to solve the minimum cardinality red domination problem for convex bipartite graphs. The algorithm presented is faster and simpler than that in the literature. Due to the asymmetry in convex bipartite graphs, the algorithm does not extend to k blue domination. We present a linear time algorithm to solve the minimum cardinality blue domination problem for convex bipartite graphs.

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Authors and Affiliations

  1. Department of Computer Science, MacEwan University, Edmonton, AB, T5J 4S2, Canada

    Nesrine Abbas

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  1. Nesrine Abbas
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Correspondence to Nesrine Abbas .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Abbas, N. (2021). Linear Algorithms for Red and Blue Domination in Convex Bipartite Graphs. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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