Optimal-time adaptive strong renaming, with applications to counting

  • Authors:

  • Dan Alistarh;James Aspnes;Keren Censor-Hillel;Seth Gilbert;Morteza Zadimoghaddam

  • Affiliations:

  • EPFL, Lausanne, Switzerland;Yale University, New Haven, CT, USA;MIT, Boston, MA, USA;National University of Singapore, Singapore, Singapore;MIT, Boston, CT, USA

  • Venue:
  • Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
  • Year:
  • 2011

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Abstract

We give two new randomized algorithms for strong renaming, both of which work against an adaptive adversary in asynchronous shared memory. The first uses repeated sampling over a sequence of arrays of decreasing size to assign unique names to each of n processes with step complexity O(log3 n). The second transforms any sorting network into a strong adaptive renaming protocol, with an expected cost equal to the depth of the sorting network. Using an AKS sorting network, this gives a strong adaptive renaming algorithm with step complexity O(log k), where k is the contention in the current execution. We show this to be optimal based on a classic lower bound of Jayanti. We also show that any such strong renaming protocol can be used to build a monotone-consistent counter with logarithmic step complexity (at the cost of adding a max register) or a linearizable fetch-and-increment register (at the cost of increasing the step complexity by a logarithmic factor).