Self-stabilizing Algorithm for Minimal $\alpha$-Dominating Set

TL;DR

This paper introduces a novel self-stabilizing algorithm for minimal alpha-dominating sets in graphs, utilizing the alpha-domination parameter for the first time in this paradigm, with proven efficiency and convergence.

Contribution

It presents the first self-stabilizing algorithm incorporating alpha-domination, demonstrating convergence and efficiency through proofs and simulations.

Findings

Converges in O(nm) moves under distributed daemon

Effective in arbitrary graphs with n nodes and m edges

Validated by simulations and mathematical proofs

Abstract

A self-stabilizing algorithm for the minimal $\alpha$-dominating set is proposed in this paper. The $\alpha$-domination parameter has not used before in self-stabilization paradigm. Using an arbitrary graph with $n$ nodes and $m$ edges, the proposed algorithm converges in $O(nm)$ moves under distributed daemon. Simulation tests and mathematical proofs show the efficiency of the algorithm.