Efficient stabilization of cooperative matching games

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

Original languageEnglish
Pages (from-to)69-82
Number of pages14
JournalTheoretical Computer Science
Volume677
DOIs
Publication statusPublished - 2017 May 16
Externally publishedYes

    Fingerprint

Keywords

  • Cooperative game
  • Core
  • Gallai–Edmonds decomposition
  • Matching
  • Network bargaining
  • Solution concept

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this