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A distributed algorithm to find k-dominating sets

L. D. Penso·V. C. Barbosa
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Abstract

We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a $k$-dominating set of minimum size is NP-hard. We give a new synchronous distributed algorithm to find a $k$-dominating set in $G$ of size no greater than $\lfloor n/(k+1)\rfloor$. Our algorithm requires $O(k\log^*n)$ time and $O(m\log k+n\log k\log^*n)$ messages to run. It has the same time complexity as the best currently known algorithm, but improves on that algorithm's message complexity and is, in addition, conceptually simpler.

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BibTeXRIS

L. D. Penso, V. C. Barbosa. 2003-09-23. A distributed algorithm to find k-dominating sets. https://doi.org/10.1016/s0166-218x(03)00368-8

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