Edge Coloring on Dynamic Graphs.

Graph edge coloring is a fundamental problem in graph theory and has been widely used in a variety of applications. Existing solutions for edge coloring mainly focus on static graphs. However, many graphs in real world are highly dynamic. Motivated by this, we study the dynamic edge coloring problem in this paper. Since edge coloring is NP-Complete, to obtain an effective dynamic edge coloring, we aim to incrementally maintain the edge coloring in a way such that the coloring result is consistent with one of the best approximate static edge coloring algorithms when the graph is dynamically updated. Unfortunately, our theoretical result shows that the problem of finding such dynamic graph edge coloring is unbounded. Despite this, we propose an efficient dynamic edge coloring algorithm that only explores the edges with color change and their 2-hop incident edges to maintain the coloring. Moreover, we propose some early pruning rules to further reduce the unnecessary computation. Experimental results on real graphs demonstrate the efficiency of our approach.