Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Frontiers of electronic commerce
Frontiers of electronic commerce
Coalitions among computationally bounded agents
Artificial Intelligence - Special issue on economic principles of multi-agent systems
Methods for task allocation via agent coalition formation
Artificial Intelligence
Introduction to Multiagent Systems
Introduction to Multiagent Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the computational complexity of qualitative coalitional games
Artificial Intelligence
On fairness in the carpool problem
Journal of Algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
On the computational complexity of coalitional resource games
Artificial Intelligence
On agent types in coalition formation problems
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Graph-based coalitional games: an analysis via characteristics
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Overlapping coalition formation games: charting the tractability frontier
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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Coalition formation is a key topic in multi--agent systems (mas). Coalitions enable agents to achieve goals that they may not have been able to achieve independently, and encourages resource sharing among agents with different goals. A range of previous studies have found that problems in coalitional games tend to be computationally complex. However, such hardness results consider the entire input as one, ignoring any structural information on the instances. In the case of coalition formation problems, this bundles together several distinct elements of the input, e.g. the agent set, the goal set, the resources, etc. In this paper we reexamine the complexity of coalition formation problems in the coalition resources game model, as a function of their distinct input elements, using the theory of parameterized complexity. The analysis shows that not all parts of the input are created equal, and that many instances of the problem are actually tractable. We show that the problems are FPT in the number of goals, implying that if the number of goals is bounded then an efficient algorithm is available. Similarly, the problems are FPT in the combination of the number of agents and resources, again implying that if these parameters are bounded, then an efficient algorithm is available. On the other hand, the problems are para-NP hard in the number of resources, implying that even if we bound the number of resources the problems (probably) remain hard. Additionally, we show that most problems are W[1]-hard in the size of the coalition of interest, indicating that there is (probably) no algorithm polynomial in all but the coalition size. The exact definitions of the parameterized complexity notions FPT, Para-NP and W[1] are provided herein.