Fast Distributed Algorithms for Brooks–Vizing Colorings

✍ Scribed by David A Grable; Alessandro Panconesi

• Book ID: 102573639
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 208 KB
• Volume: 37
• Category: Article
• ISSN: 0196-6774
• DOI: 10.1006/jagm.2000.1097

✦ Synopsis

Let G be a ⌬-regular graph with n vertices and girth at least 4 such that ⌬ 4 log n. We give very simple, randomized, distributed algorithms for vertex Ž . coloring G with ⌬rk colors in O k q log n communication rounds, where k s Ž . O log ⌬ . The algorithm may fail or exceed the above running time, but the Ž . probability that this happens is o 1 , a quantity that goes to zero as n grows. The probabilistic analysis relies on a powerful generalization of Azuma's martingale inequality that we dub the Method of Bounded Variances.