Distributed Dominating Sets on Grids

TL;DR

This paper introduces a distributed algorithm for near-optimal dominating sets on grid graphs, extending existing centralized methods to distributed settings and generalizing for k-distance domination.

Contribution

It adapts a centralized grid dominating set algorithm into a distributed version and generalizes it for k-distance domination problems.

Findings

Distributed algorithm achieves near-optimal dominating sets.

Size of dominating sets is within a small bound of the optimal.

Algorithm applies to generalized k-distance domination.

Abstract

This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids. The size of the dominating set provided by this centralized algorithm is upper-bounded by $\lceil\frac{(m+2)(n+2)}{5}\rceil$ for $m\times n$ grids and its difference from the optimal domination number of the grid is upper-bounded by five. Both the centralized and distributed algorithms are generalized for the $k$-distance dominating set problem, where all grid vertices are within distance $k$ of the vertices in the dominating set.