On the Complexity of Nucleolus Computation for Bipartite b-Matching Games
Computer Science and Game Theory
2025-10-15 v3 Computational Complexity
Data Structures and Algorithms
Abstract
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 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 b(v) = 2 as well as an efficient algorithm for computing the non-simple b-matching nucleolus when b = 2.
Cite
@article{arxiv.2105.07161,
title = {On the Complexity of Nucleolus Computation for Bipartite b-Matching Games},
author = {Jochen Koenemann and Justin Toth and Felix Zhou},
journal= {arXiv preprint arXiv:2105.07161},
year = {2025}
}