Time and space lower bounds for implementations using k-cAS

Hagit Attiya, Danny Hendler

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper presents lower bounds on the time and space complexity of implementations that use k-compare&swap (k-CAS) synchronization primitives. We prove that using k-CAS primitives can improve neither the time nor the space complexity of implementations of widely used concurrent objects, such as counter, stack, queue, and collect. Surprisingly, overly restrictive use of k-CAS may even increase the space complexity required by such implementations. We prove a lower bound of Ω (log2n) on the round complexity of implementations of a collect object using read, write, and k-CAS, for any k, where n is the number of processes in the system. There is an implementation of collect with O(log2n) round complexity that uses only reads and writes. Thus, our lower bound establishes that k-CAS is no stronger than read and write for collect implementation round complexity. For k-CAS operations that return the values of all the objects they access, we prove that the total step complexity of implementing key objects such as counters, stacks, and queues is Ω (n logkn). We also prove that k-CAS cannot improve the space complexity of implementing many objects (including counter, stack, queue, and single-writer snapshot). An implementation has to use at least n base objects even if k-CAS is allowed, and if all operations (other than read) swap exactly k base objects, then it must use at least k ̇ n base objects.

Original languageEnglish
Article number4815228
Pages (from-to)162-173
Number of pages12
JournalIEEE Transactions on Parallel and Distributed Systems
Issue number2
StatePublished - 1 Feb 2010


  • Collect
  • Compare&swap (CAS)
  • Conditional synchronization primitives
  • Counter
  • K-compare&swap (k-CAS)
  • Queue
  • Round complexity
  • Stack

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Computational Theory and Mathematics


Dive into the research topics of 'Time and space lower bounds for implementations using k-cAS'. Together they form a unique fingerprint.

Cite this