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...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science Vol. 998; p. 114476
Main Authors: Könemann, Jochen, Toth, Justin, Zhou, Felix
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2024
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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