On a random walk problem arising in self-stabilizing token management
PODC '91 Proceedings of the tenth annual ACM symposium on Principles of distributed computing
Meeting times of random walks on graphs
Information Processing Letters
Probability Models for Computer Science
Probability Models for Computer Science
Coverage-adaptive random walks for fast sensory data collection
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
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We study here dynamic antagonism in a fixed network, represented as a graph G of n vertices. In particular, we consider the case of k ≤n particles walking randomly independently around the network. Each particle belongs to exactly one of two antagonistic species, none of which can give birth to children. When two particles meet, they are engaged in a (sometimes mortal) local fight. The outcome of the fight depends on the species to which the particles belong. Our problem is to predict (i.e. to compute) the eventual chances of species survival. We prove here that this can indeed be done in expected polynomial time on the size of the network, provided that the network is undirected.