Self-Stabilizing Algorithms in the Uniform Port Model

2026-07-09

AI Summary

This work addresses the efficient resolution of local symmetry-breaking problems—such as maximal independent set, maximum matching, sinkless orientation, and vertex/edge k-coloring—in a truly uniform distributed computing model. To this end, the authors introduce the Uniform Port Model, which leverages constant-size finite-state automata deployed on graph half-edges to enable uniform computation, augmented with a half-edge labeling mechanism. Within this framework, they present the first self-stabilizing algorithm that operates in polylogarithmic time for general graphs, substantially broadening the class of problems that can be efficiently expressed and solved in a genuinely uniform distributed setting.

Abstract

We introduce a distributed computational model referred to as the \emph{uniform port} model. An algorithm operating in this model is defined by means of local automata associated with the ports (a.k.a.\ half-edges) of the input graph. The crux of the uniform port model is that a single constant-size finite automaton is hosted by every port of every graph, making the model \emph{truly uniform}. Moreover, since the new model explicitly supports the assignment of (input and) output labels to the graph's (half-)edges, it facilitates natural formulations of (half-)edge-labeling problems such as maximal matching and sinkless orientation, which are outside the expressivity scope of prior node-centric truly uniform distributed computational models. The main technical contribution of this paper is the design of efficient (i.e., with poly-logarithmic runtime) \emph{self-stabilizing} uniform port algorithms, operating on general graphs, for various fundamental local symmetry breaking problems, including maximal independent set, maximal matching, sinkless orientation, and maximal node/edge $k$-coloring. While efficient self-stabilizing algorithms for local symmetry breaking problems have been extensively studied in stronger computational models, our work is the first to demonstrate the existence of such algorithms in a truly uniform model.

Problem

• self-stabilizing
• uniform port model
• local symmetry breaking
• distributed algorithms
• edge-labeling problems

Innovation

• uniform port model
• self-stabilizing algorithms
• distributed computing
• symmetry breaking
• edge-labeling problems