A distributed algorithm to find k-dominating sets

TL;DR

This paper presents a new distributed algorithm for finding a k-dominating set in a graph, which is simpler and more message-efficient than previous algorithms while maintaining optimal time complexity.

Contribution

The paper introduces a novel synchronous distributed algorithm for k-dominating sets with improved message complexity and conceptual simplicity.

Findings

Achieves a k-dominating set of size at most ⌊n/(k+1)⌋

Runs in O(k log* n) time, matching the best known time complexity

Reduces message complexity compared to previous algorithms

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.