Fast Distributed Algorithms for Brooks–Vizing Colorings
Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G with Δ/k colors in O(k+logn) communication rounds, where k=O(logΔ). The algorithm may fail or exceed the above running time, but the probabi...
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| Veröffentlicht in: | Journal of algorithms Jg. 37; H. 1; S. 85 - 120 |
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| Abstract | Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G with Δ/k colors in O(k+logn) communication rounds, where k=O(logΔ). The algorithm may fail or exceed the above running time, but the 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. |
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| AbstractList | Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G with Δ/k colors in O(k+logn) communication rounds, where k=O(logΔ). The algorithm may fail or exceed the above running time, but the 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. |
| Author | Grable, David A Panconesi, Alessandro |
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| Cites_doi | 10.37236/1296 10.1007/3-540-59175-3_90 10.1109/SFCS.1989.63504 10.1016/0022-0000(93)90033-S 10.1016/S0304-3975(98)00022-X 10.1016/0196-6774(88)90006-5 10.1017/S0963548300001528 10.1137/0403008 10.1016/0304-3975(89)90121-7 10.1007/BF02773639 10.1016/S0020-0190(99)00064-2 10.1016/0012-365X(78)90102-4 10.1145/103418.103443 10.1007/BF01200759 10.1006/jagm.1996.0017 10.1002/(SICI)1098-2418(199705)10:3<385::AID-RSA6>3.0.CO;2-S 10.1017/S0963548397003246 10.1137/1.9781611970029 |
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| Keywords | Bounded variance method Randomization Brooks Vizing like problem Distributed algorithm Graph colouring Graph theory Complexity measure Bounded solution Azuma martingale inequality |
| Language | English |
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| Snippet | Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph theory Mathematics Sciences and techniques of general use Theoretical computing |
| Title | Fast Distributed Algorithms for Brooks–Vizing Colorings |
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