Fault Tolerant Coloring of the Asynchronous Cycle
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We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle C_n, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of n ≥ 3, and runs in O(log^* n) rounds in C_n. This round-complexity is optimal thanks to a known matching lower bound, which applies even to synchronous (failure-free) executions. The range of colors used by our algorithm, namely {0, ..., 4}, is optimal too, thanks to a known lower bound on the minimum number of names for which renaming is solvable wait-free in shared-memory systems, whenever n is a power of a prime. Indeed, our model coincides with the shared-memory model whenever n = 3, and the minimum number of names for which renaming is possible in 3-process shared-memory systems is 5.
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