Move Complexity of a Self-Stabilizing Algorithm for Maximal Independent Sets

TL;DR

This paper analyzes the move complexity of a self-stabilizing algorithm for maximal independent sets, revealing that under certain conditions, its move count can grow faster than polynomially with graph size.

Contribution

It demonstrates that the move complexity of the ${ mf deg}$ algorithm is unbounded by polynomial functions under the central scheduler.

Findings

Move complexity is not polynomially bounded under the central scheduler.

The algorithm guarantees a maximal independent set with approximation ratio $( riangle + 2)/3$.

Provides insights into the limitations of self-stabilizing algorithms in terms of move complexity.

Abstract

${\cal A}_\mathsf{deg}$ is a self-stabilizing algorithm that computes a maximal independent set in a finite graph with approximation ratio $(\Delta + 2)/3$. In this note we show that under the central scheduler the number of moves of ${\cal A}_\mathsf{deg}$ is not bounded by a polynomial in $n$.