Perfect matching in bipartite hypergraphs subject to a demand graph

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....

Full description

Saved in:
Bibliographic Details
Published inAnnals of operations research Vol. 321; no. 1-2; pp. 39 - 48
Main Authors Aronshtam, Lior, Ilani, Hagai, Shufan, Elad
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2023
Springer
Springer Nature B.V
Subjects
Assignment problem
Business and Management
Combinatorics
Demand
Demand (Economics)
Graph matching
Graph theory
Graphs
Matching theory
Operations research
Operations Research/Decision Theory
Original Research
Tenants
Theory of Computation
Israel
Assignment
Perfect matching
Bipartite hypergraph
Online AccessGet full text

Cover

More Information
Summary: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 Ω ( n 1 / k ) , for some constant 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-022-05073-9