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arXiv · 2503.06017

Welfare Approximation in Additively Separable Hedonic Games

Martin Bullinger·Vaggos Chatziafratis·Parnian Shahkar
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Abstract

Partitioning a set of $n$ items or agents while maximizing the value of the partition is a fundamental algorithmic task. We study this problem in the specific setting of maximizing social welfare in additively separable hedonic games. Unfortunately, this task faces strong computational boundaries: Extending previous results, we show that approximating welfare by a factor of $n^{1-\epsilon}$ is NP-hard, even for severely restricted weights. However, we can obtain a randomized $\log n$-approximation on instances for which the sum of input valuations is nonnegative. Finally, we study two stochastic models of aversion-to-enemies games, where the weights are derived from Erd\H{o}s-R\'{e}nyi or multipartite graphs. We obtain constant-factor and logarithmic-factor approximations with high probability.

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BibTeXRIS

Martin Bullinger, Vaggos Chatziafratis, Parnian Shahkar. 2025-03-08. Welfare Approximation in Additively Separable Hedonic Games. https://arxiv.org/abs/2503.06017

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