The Expected Size of the Rule k Dominating Set

TL;DR

This paper estimates the expected size of the Rule k dominating set in random unit disk graphs, providing insights into its efficiency in geometric network models.

Contribution

It introduces an estimation method for the expected size of Rule k dominating sets in random geometric graphs, a novel analysis in this context.

Findings

Derived an expected size formula for Rule k dominating sets

Analyzed the behavior in random unit disk graph models

Provided bounds and asymptotic results

Abstract

Rule k is a localized approximation algorithm that finds a small connected dominating set in a graph. We estimate the expected size of the Rule k dominating set for the model of random unit disk graphs constructed from n random points in an s_n by s_n square region of the plane.