Self-Stabilizing Algorithms in the Uniform Port Model

Abstract

We introduce a distributed computational model referred to as the 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 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) 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.