STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Locality in distributed graph algorithms
SIAM Journal on Computing
The distributed bit complexity of the ring: from the anonymous to the non-anonymous case
Information and Computation
Communication complexity
Simple distributed&Dgr; + 1-coloring of graphs
Information Processing Letters
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Bit complexity of breaking and achieving symmetry in chains and rings
Journal of the ACM (JACM)
About randomised distributed graph colouring and graph partition algorithms
Information and Computation
Distributed coloring in Õ (√log n) Bit Rounds
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
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We present and analyse a very simple randomised distributed vertex colouring algorithm for ring graphs. Its time complexity is log"2n+o(logn) on average and 2log"2n+o(logn) with probability 1-o(n^-^1). Since each message contains one bit, we deduce the same values for its bit complexity. Then we combine this algorithm with another and we obtain a 3-colouring algorithm for ring graphs. Thanks to an overlapping, we obtain once more the same values for the time complexities on average and with probability 1-o(n^-^1). The same results hold for the bit complexity. These results are obtained using the Mellin transform. We establish lower bounds (on average and with probability 1-o(n^-^1)) for the distributed randomised anonymous ring colouring problem. We prove that our algorithms match these lower bounds modulo a negligible additive function (negligible with respect to log"2n). We assume that the ring is anonymous: unique identities are not available to distinguish the processes; we only assume that each vertex distinguishes between its neighbours. Furthermore, we do not assume that the size (or an upper bound on the size) of the ring is known.