A parameterized point of view on forming small coalitions - Optimisation Combinatoire
Pré-Publication, Document De Travail Année : 2024

A parameterized point of view on forming small coalitions

Harmender Gahlawat
Nikolaos Melissinos
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Résumé

Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition Formation} problem. Here, we study a version of this problem where each team must additionally be of bounded size. We conduct a systematic algorithmic study, providing several intractability results as well as multiple exact algorithms that scale well as the input grows (FPT), which could prove useful in practice. Our main contribution is an algorithm that deals efficiently with tree-like structures (bounded \emph{treewidth}) for ``small'' teams. We complement this result by proving that our algorithm is asymptotically optimal. Particularly, even considering star-like structures (bounded \emph{vertex cover number}) cannot result in an algorithm with a better running time, under reasonable theoretical assumptions.
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Dates et versions

hal-04562753 , version 1 (29-04-2024)

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  • HAL Id : hal-04562753 , version 1

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Foivos Fioravantes, Harmender Gahlawat, Nikolaos Melissinos. A parameterized point of view on forming small coalitions. 2024. ⟨hal-04562753⟩
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