The space complexity of long-lived and one-shot timestamp implementations

  • Authors:

  • Maryam Helmi;Lisa Higham;Eduardo Pacheco;Philipp Woelfel

  • Affiliations:

  • University of Calgary, Calgary, AB, Canada;University of Calgary, Calgary, AB, Canada;Universidad Nacional Autonoma de Mexico, Mexico D.F., Mexico;University of Calgary, Calgary, AB, Canada

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

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Abstract

This paper is concerned with the problem of implementing an unbounded timestamp object from multi-writer atomic registers, in an asynchronous distributed system of n processors with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen, Fatourou and Ruppert [7] showed that √n/2-O(1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processors can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of n/6 - O(1) registers for the obstruction-free long-lived timestamp problem. Previous such linear lower bounds were only known for constrained versions of the timestamp problem. This bound is asymptotically tight; Ellen, Fatourou and Ruppert [7] constructed a wait-free algorithm that uses n-1 registers. Second we show that √(n)-O(1) registers are required for any obstruction-free implementation of one-shot timestamp systems (meaning each processor can get a timestamp at most once). We show that this bound is also asymptotically tight by providing a wait-free one-shot timestamp system that uses fewer than 2√n registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.