Weak graph colorings: distributed algorithms and applications

We study deterministic, distributed algorithms for two weak variants of the standard graph coloring problem. We consider defective colorings, i.e., colorings where nodes of a color class may induce a graph of maximum degree d for some parameter d > 0. We also look at colorings where a minimum number of multi-chromatic edges is required. For an integer k > 0, we call a coloring k-partially proper if every node v has at least min{k, deg(v)} neighbors with a different color We show that for all d ∈ {1, . . . , ∆}, it is possible to compute a O(∆2 /d2 )-coloring with defect d in time O(log∗ n) where ∆ is the largest degree of the network graph. Similarly, for all k ∈ {1, . . . , ∆}, a k-partially proper O(k2 )-coloring can be computed in O(log∗ n) rounds. As an application of our weak defective coloring algorithm, we obtain a faster deterministic algorithm for the standard vertex coloring problem on graphs with moderate degrees. We show that in time O(∆ + log∗ n...

• Type: Conference
• Year: 2009
• Where: SPAA
• Authors: Fabian Kuhn
• Keywords: Parallel Computing, SPAA 2009