On the complexity of nucleolus computation for bipartite b-matching games

We explore the complexity of nucleolus computation in b-matching games on bipartite graphs. We show that computing the nucleolus of a simple b-matching game is NP-hard when b≡3 even on bipartite graphs of maximum degree 7. We complement this with partial positive results in the special case where b...

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Vydáno v:Theoretical computer science Ročník 998; s. 114476
Hlavní autoři: Könemann, Jochen, Toth, Justin, Zhou, Felix
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2024
Témata:
Algorithmic game theory
Combinatorial optimization
Complexity theory
Cooperative game theory
Linear programming
Matching games
Linear programming
Complexity theory
Matching games
Combinatorial optimization
Algorithmic game theory
Cooperative game theory
ISSN:0304-3975, 1879-2294
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Shrnutí:We explore the complexity of nucleolus computation in b-matching games on bipartite graphs. We show that computing the nucleolus of a simple b-matching game is NP-hard when b≡3 even on bipartite graphs of maximum degree 7. We complement this with partial positive results in the special case where b values are bounded by 2. In particular, we describe an efficient algorithm when a constant number of vertices satisfy bv=2 as well as an efficient algorithm for computing the non-simple b-matching nucleolus when b≡2. •We explore the complexity of nucleolus computation in b-matching games on bipartite graphs.•Computing the nucleolus of a simple b-matching game is NP-hard when b=3 even on bipartite graphs of maximum degree 7.•We complement this with partial positive results in the special case where b values are bounded by 2.•In particular, we describe an efficient algorithm when a constant number of vertices satisfy bv=2.•Also an efficient algorithm for computing the non-simple b-matching nucleolus when b=2.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114476