scholarly journals Efficient Coalition Structure Generation via Approximately Equivalent Induced Subgraph Games

2021 ◽  
pp. 1-11
Author(s):  
Filippo Bistaffa ◽  
Georgios Chalkiadakis ◽  
Alessandro Farinelli
Keyword(s):  
Coalition Structure ◽  
Structure Generation ◽  
Induced Subgraph ◽  
Coalition Structure Generation

scholarly journals Coalition Structure Generation over Graphs

2012 ◽  
Vol 45 ◽  
pp. 165-196 ◽  
Author(s):  
T. Voice ◽  
M. Polukarov ◽  
N. R. Jennings
Keyword(s):  
Linear Time ◽  
Coalition Structure ◽  
Valuation Function ◽  
Structure Generation ◽  
Induced Subgraph ◽  
Bounded Treewidth ◽  
Vertex Separator ◽  
Np Complete ◽  
Minor Free Graphs ◽  
Coalition Structure Generation

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components’ values. This problem is generally NP–complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members—that is, two nodes have no effect on each other’s marginal con- tribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor–free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP–complete for planar graphs, and hence, for any K_k minor–free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m^2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph.

Robust Coalition Structure Generation

2018 ◽  
pp. 140-157
Author(s):  
Tenda Okimoto ◽  
Nicolas Schwind ◽  
Emir Demirović ◽  
Katsumi Inoue ◽  
Pierre Marquis
Keyword(s):  
Coalition Structure ◽  
Structure Generation ◽  
Coalition Structure Generation

scholarly journals On the Online Coalition Structure Generation Problem

2021 ◽  
Vol 72 ◽  
pp. 1215-1250
Author(s):  
Michele Flammini ◽  
Gianpiero Monaco ◽  
Luca Moscardelli ◽  
Mordechai Shalom ◽  
Shmuel Zaks
Keyword(s):  
Online Algorithm ◽  
Coalition Structure ◽  
Weight Functions ◽  
Value Functions ◽  
Multi Agent Systems ◽  
Structure Generation ◽  
Coalition Structures ◽  
Multi Agent ◽  
Coalition Structure Generation ◽  
Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

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