Distributed edge coloration for bipartite networks

Abstract

This paper presents a self-stabilizing algorithm to color the edges of a bipartite network such that any two adjacent edges receive distinct colors. The algorithm has the self-stabilizing property; it works without initializing the system. It also works in a de-centralized way without a leader computing a proper coloring for the whole system. Moreover, it finds an optimal edge coloring and its time complexity is O(n 2 k + m) moves, where k is the number of edges that are not properly colored in the initial configuration.

A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs

“…The edge-coloring problem consists in assigning colors to the graph edges such that every two adjacent edges have different colors. A self-stabilizing algorithm for this problem has been proposed by Huang and Tzeng [34], and a second one has been proposed recently by Tzeng et al [68]. This latter algorithm finds a (∆ + 4)-edge coloring in planar graphs, while the former algorithm is designed for bipartite graphs.…”