Randomized loose renaming in o(log log n) time

  • Authors:

  • Dan Alistarh;James Aspnes;George Giakkoupis;Philipp Woelfel

  • Affiliations:

  • MIT, Cambridge, MA, USA;Yale University, New Haven, CT, USA;INRIA Rennes -- Bretagne Atlantique, Rennes, France;Department of Computer Science, Calgary, AB, Canada

  • Venue:
  • Proceedings of the 2013 ACM symposium on Principles of distributed computing
  • Year:
  • 2013

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Abstract

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 with O( log log n ) (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. We also present a variant of the adaptive algorithm which requires O( k log log k ) total process steps. All upper bounds hold with high probability against a strong adaptive adversary. We complement the algorithms with an Ω(log log n) 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. Since our algorithms use O(n) test-and-set objects, our results provide matching bounds on the cost of loose renaming in this setting.