Dynamic edge coloring with improved approximation

Abstract

Given an undirected simple graph G = (V, E) that undergoes edge insertions and deletions, we wish to efficiently maintain an edge coloring with only a few colors. The previous best dynamic algorithm by [3] could deterministically maintain a valid edge coloring using 2∆−1 colors with O(log ∆) update time, where ∆ stands for the current maximum vertex degree of graph G. In this paper, we first propose a new static (1 + )∆ edge coloring algorithm that runs in near-linear time. Based on this static algorithm, we show that there is a randomized dynamic algorithm for this problem that only uses (1+)∆ colors with O(log8 n/4) amortized update time when ∆ ≥ Ω(log2 n/2), where > 0 is an arbitrarily small constant.