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Abstract: The graph theoretic concept of maximal independent set arises in severalpractical problems in computer science as well as in game theory. A maximalindependent set is defined by the set of occupied nodes that satisfy somepacking and covering constraints. It is known that finding minimum andmaximum-density maximal independent sets are hard optimization problems. Inthis paper, we use cavity method of statistical physics and Monte Carlosimulations to study the corresponding constraint satisfaction problem onrandom graphs. We obtain the entropy of maximal independent sets within thereplica symmetric and one-step replica symmetry breaking frameworks, sheddinglight on the metric structure of the landscape of solutions and suggesting aclass of possible algorithms. This is of particular relevance for theapplication to the study of strategic interactions in social and economicnetworks, where maximal independent sets correspond to pure Nash equilibria ofa graphical game of public goods allocation.



Author: L. Dall'Asta, P. Pin, A. Ramezanpour

Source: https://arxiv.org/







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