TY - GEN

T1 - Efficient stabilization of cooperative matching games

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Okamoto, Yoshio

N1 - Funding Information:
Supported by JSPS KAKENHI Grant Numbers 25330003, 15H00849. Supported by JST, ERATO, Kawarabayashi Large Graph Project, and by JSPS KAKENHI Grant Numbers 25730001, Supported by JST, PRESTO. Supported by JST, ERATO, Kawarabayashi Large Graph Project, and by JSPS KAKENHI Grant Numbers 24106002, 24700004. Supported by JSPS KAKENHI Grant Numbers 24106005, 24700008, 24220003, 15K00009.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:85014285231

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 41

EP - 49

BT - AAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

T2 - 15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016

Y2 - 9 May 2016 through 13 May 2016

ER -