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Sub-logarithmic Randomized Loose Renaming

Renaming is a classic distributed coordination task in which a set of processes must pick distinct identifiers from a small namespace. In this paper, we consider the time complexity of this problem when the namespace is linear in the number of participants, a variant known as loose renaming. We give a non-adaptive algorithm withO(log logn) (individual) step complexity, where n is a known upper bound on contention, and an adaptive algorithm with step complexity O((log log k)2), where k is the actual contention in the execution. Both bounds hold with high probability against a strong adaptive adversary. The running time improvement over previously known solutions is exponential. We complement the algorithms with an Ω(log logn) expected time lower bound on the complexity of randomized renaming using test-and-set operations and linear space. The result is based on a new coupling technique, and is the first to apply to non-adaptive randomized renaming.