### Abstract

Forming effective coalitions is a major research challenge in AI and multi-agent systems (MAS). Coalition Structure Generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a coalition structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume that the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, one might imagine that the computational costs required in this approach would be too expensive, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve O (2 ^{n}) DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS with quality guarantees. More specifically, we develop an algorithm with parameter k that can find a CS whose social surplus is at least max(k/w* + 1), k/[n/2/) of the optimal CS, where w* is the tree width of a constraint graph. When k = 1, the complexity of this algorithm is about the same as solving just one DCOP. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing an efficient CSG algorithm with quality guarantees.

Original language | English |
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Title of host publication | AAAI-10 / IAAI-10 - Proceedings of the 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference |

Pages | 197-203 |

Number of pages | 7 |

Volume | 1 |

Publication status | Published - 2010 |

Event | 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference, AAAI-10 / IAAI-10 - Atlanta, GA, United States Duration: Jul 11 2010 → Jul 15 2010 |

### Other

Other | 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference, AAAI-10 / IAAI-10 |
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Country | United States |

City | Atlanta, GA |

Period | 7/11/10 → 7/15/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Artificial Intelligence

### Cite this

*AAAI-10 / IAAI-10 - Proceedings of the 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference*(Vol. 1, pp. 197-203)

**Coalition structure generation based on distributed constraint optimization.** / Ueda, Suguru; Iwasaki, Atsushi; Yokoo, Makoto; Calin Silaghi, Marius; Hirayama, Katsutoshi; Matsui, Toshihiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AAAI-10 / IAAI-10 - Proceedings of the 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference.*vol. 1, pp. 197-203, 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference, AAAI-10 / IAAI-10, Atlanta, GA, United States, 7/11/10.

}

TY - GEN

T1 - Coalition structure generation based on distributed constraint optimization

AU - Ueda, Suguru

AU - Iwasaki, Atsushi

AU - Yokoo, Makoto

AU - Calin Silaghi, Marius

AU - Hirayama, Katsutoshi

AU - Matsui, Toshihiro

PY - 2010

Y1 - 2010

N2 - Forming effective coalitions is a major research challenge in AI and multi-agent systems (MAS). Coalition Structure Generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a coalition structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume that the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, one might imagine that the computational costs required in this approach would be too expensive, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve O (2 n) DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS with quality guarantees. More specifically, we develop an algorithm with parameter k that can find a CS whose social surplus is at least max(k/w* + 1), k/[n/2/) of the optimal CS, where w* is the tree width of a constraint graph. When k = 1, the complexity of this algorithm is about the same as solving just one DCOP. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing an efficient CSG algorithm with quality guarantees.

AB - Forming effective coalitions is a major research challenge in AI and multi-agent systems (MAS). Coalition Structure Generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a coalition structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume that the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, one might imagine that the computational costs required in this approach would be too expensive, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve O (2 n) DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS with quality guarantees. More specifically, we develop an algorithm with parameter k that can find a CS whose social surplus is at least max(k/w* + 1), k/[n/2/) of the optimal CS, where w* is the tree width of a constraint graph. When k = 1, the complexity of this algorithm is about the same as solving just one DCOP. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing an efficient CSG algorithm with quality guarantees.

UR - http://www.scopus.com/inward/record.url?scp=77958597023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958597023&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781577354642

VL - 1

SP - 197

EP - 203

BT - AAAI-10 / IAAI-10 - Proceedings of the 24th AAAI Conference on Artificial Intelligence and the 22nd Innovative Applications of Artificial Intelligence Conference

ER -