# A Branch and Price Algorithm for Coalition Structure Generation over Graphs

### Emanuel Olariu, Cristian FrÄƒsinaru, Policiuc Albert

#### Abstract

This paper presents an integer linear programming approach for the coalition structure generation (CSG) problem over graphs. Forming such structures is a major problem in areas like artificial intelligence an multi-agent systems. The problem asks to partition a given set of agents into coalitions in order to maximize their social well-fare - the agents being vertices in a given graph and their communication links being the edges. We give a truncated branch and price algorithm using valuation functions for which this problem is proven to be computationally hard. We consider three cases: first when the value of a coalition is the sum of the weights of its edges, second when the value takes account of both inter- and intra-coalitional disagreements and agreements, respectively, and another one when the value takes account of the pairs of adjacent agents which have common neighbors outside. The experimental results cover sets of up to fifty agents. Our approach prove that an off the shelf optimization solver can be used to solve CSG problem over graphs for some of the most used valuation functions. We prove also that for the coordination valuation the corresponding decision problem is NP-complete when the number of coalitions must be two.

Download#### Paper Citation

#### in Harvard Style

Olariu E., FrÄƒsinaru C. and Albert P. (2021). **A Branch and Price Algorithm for Coalition Structure Generation over Graphs**.In *Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-484-8, pages 390-397. DOI: 10.5220/0010316303900397

#### in Bibtex Style

@conference{icaart21,

author={Emanuel Olariu and Cristian FrÄƒsinaru and Policiuc Albert},

title={A Branch and Price Algorithm for Coalition Structure Generation over Graphs},

booktitle={Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2021},

pages={390-397},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010316303900397},

isbn={978-989-758-484-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - A Branch and Price Algorithm for Coalition Structure Generation over Graphs

SN - 978-989-758-484-8

AU - Olariu E.

AU - FrÄƒsinaru C.

AU - Albert P.

PY - 2021

SP - 390

EP - 397

DO - 10.5220/0010316303900397