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• W2934894069 abstract "We consider cooperation among insects, modeled as cooperation between mobile robots on a graph. Within this setting, we consider the problem of mobile robot dispersion on graphs. The study of mobile robots on a graph is an interesting paradigm with many interesting problems and applications. The problem of dispersion in this context, introduced by Augustine and Moses Jr., asks that $n$ robots, initially placed arbitrarily on an $n$ node graph, work together to quickly reach a configuration with exactly one robot at each node. Previous work on this problem has looked at the trade-off between the time to achieve dispersion and the amount of memory required by each robot. However, the trade-off was analyzed for textit{deterministic algorithms} and the minimum memory required to achieve dispersion was found to be $Omega(log n)$ bits at each robot. In this paper, we show that by harnessing the power of textit{randomness}, one can achieve dispersion with $O(log Delta)$ bits of memory at each robot, where $Delta$ is the maximum degree of the graph. Furthermore, we show a matching lower bound of $Omega(log Delta)$ bits for any textit{randomized algorithm} to solve dispersion. We further extend the problem to a general $k$-dispersion problem where $k> n$ robots need to disperse over $n$ nodes such that at most $lceil k/n rceil$ robots are at each node in the final configuration." @default.
• W2934894069 created "2019-04-11" @default.
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• W2934894069 date "2019-01-01" @default.
• W2934894069 modified "2023-10-05" @default.
• W2934894069 title "Dispersion of Mobile Robots: The Power of Randomness" @default.
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• W2934894069 doi "https://doi.org/10.1007/978-3-030-14812-6_30" @default.
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