Fully Lattice Linear Algorithms

TL;DR

This paper introduces fully lattice linear algorithms that induce multiple lattices and provide a self-stabilizing solution for the minimal dominating set problem, advancing the understanding of lattice linear problem-solving.

Contribution

It defines a new class of algorithms called fully lattice linear algorithms that induce multiple lattices and demonstrates a self-stabilizing algorithm for minimal dominating set.

Findings

Algorithms induce multiple lattices with partial order among states

Initial states lock into one of the lattices

Provides a self-stabilizing solution for minimal dominating set

Abstract

This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they induce a partial order among all states and form \textit{multiple lattices}. An initial state locks in one of these lattices. We present a lattice linear self-stabilizing algorithm for minimal dominating set.