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Perfect matching in bipartite hypergraphs subject to a demand graph

Author

Listed:
  • Lior Aronshtam

    (SCE – Shamoon College of Engineering)

  • Hagai Ilani

    (SCE – Shamoon College of Engineering)

  • Elad Shufan

    (SCE – Shamoon College of Engineering)

Abstract

Motivated by the problem of assigning plots to tenants, we present a version of the bipartite hypergraph matching problem. This version deals with a hypergraph with a constraint on its hyperedges, defined by a demand graph. We study the complexity of the matching problem for different demand graphs. The matching problem for 3-uniform hypergraphs is polynomially solvable if the set of perfect matchings of the demand graph can be polynomially generated. On the other hand, when the number of disjoint even cycles in the demand graph is $$\varvec{\Omega (n^{1/k})}$$ Ω ( n 1 / k ) , for some constant $$\varvec{k}$$ k , the matching problem is NP-complete. For non-uniform hypergraphs, we show that the problem is NP-complete, even for very simple demand graphs.

Suggested Citation

  • Lior Aronshtam & Hagai Ilani & Elad Shufan, 2023. "Perfect matching in bipartite hypergraphs subject to a demand graph," Annals of Operations Research, Springer, vol. 321(1), pages 39-48, February.
    • Handle: RePEc:spr:annopr:v:321:y:2023:i:1:d:10.1007_s10479-022-05073-9
    DOI: 10.1007/s10479-022-05073-9
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    References listed on IDEAS

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    1. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(4), pages 1585-1632.
    2. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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