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This paper introduces the uniform port model, a distributed computational framework where each port of an input graph hosts a constant-size finite automaton, enabling the formulation of edge-labeling problems that were previously outside the reach of node-centric models. The authors design efficient self-stabilizing algorithms for fundamental local symmetry breaking problems, achieving poly-logarithmic runtime on general graphs. This work is significant as it is the first to establish the existence of efficient self-stabilizing algorithms within a truly uniform model, expanding the capabilities of distributed computing in graph theory.
Efficient self-stabilizing algorithms for local symmetry breaking problems can now be executed in a truly uniform distributed model, challenging previous limitations in computational expressivity.
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.
