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 - May 16 2017

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Stabilization
Game
Bargaining
NP-complete problem
Vertex of a graph
Combinatorial optimization
Combinatorial Optimization Problem
Networking
Polynomial time
Polynomials
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Efficient stabilization of cooperative matching games. / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio.

In: Theoretical Computer Science, Vol. 677, 16.05.2017, p. 69-82.

Research output: Contribution to journalArticle

Ito, Takehiro ; Kakimura, Naonori ; Kamiyama, Naoyuki ; Kobayashi, Yusuke ; Okamoto, Yoshio. / Efficient stabilization of cooperative matching games. In: Theoretical Computer Science. 2017 ; Vol. 677. pp. 69-82.
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