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Finding a b-matching that embeds the maximum number of edge pairs in a given set

Author

Listed:
  • Siraphob Buahong

    (Chiang Mai University)

  • Vorapong Suppakitpaisarn

    (The University of Tokyo)

  • Piyashat Sripratak

    (Chiang Mai University)

Abstract

Given a set of edge pairs in a complete bipartite graph, the objective of the maximum edge-pair embedding bipartite b-matching problem (MEEBbM) is to find a bipartite b-matching that includes the maximum number of these edge pairs. The original problem, known as the maximum edge-pair embedding bipartite matching, was demonstrated to be NP-hard and inapproximable by Nguyen et al. in 2021. Building on this, and being inspired by the optimization of reconfigurable networks, we extend the problem in this paper to consider b-matchings, with a focus on scenarios where the number of edge pairs per node is bounded. Let $$ k $$ k represent the maximum number of edge pairs that can be incident on a single node. We prove that when $$k > b$$ k > b , the problem is NP-hard. For the case when $$b = 2$$ b = 2 , we provide an exact algorithm for $$k = 1,2$$ k = 1 , 2 . Additionally, for any values of k and b, we provide a $$\Theta (k)$$ Θ ( k ) -approximation algorithm for this problem.

Suggested Citation

  • Siraphob Buahong & Vorapong Suppakitpaisarn & Piyashat Sripratak, 2025. "Finding a b-matching that embeds the maximum number of edge pairs in a given set," Journal of Combinatorial Optimization, Springer, vol. 49(5), pages 1-15, July.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:5:d:10.1007_s10878-025-01305-3
    DOI: 10.1007/s10878-025-01305-3
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    References listed on IDEAS

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