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 language | English |
|---|---|
| Pages (from-to) | 69-82 |
| Number of pages | 14 |
| Journal | Theoretical Computer Science |
| Volume | 677 |
| DOIs | |
| Publication status | Published - May 16 2017 |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Efficient stabilization of cooperative matching games
AU - Ito, Takehiro
AU - Kakimura, Naonori
AU - Kamiyama, Naoyuki
AU - Kobayashi, Yusuke
AU - Okamoto, Yoshio
PY - 2017/5/16
Y1 - 2017/5/16
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.
UR - http://www.scopus.com/inward/record.url?scp=85017340165&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85017340165&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2017.03.020
DO - 10.1016/j.tcs.2017.03.020
M3 - Article
AN - SCOPUS:85017340165
VL - 677
SP - 69
EP - 82
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
ER -