Tight RMR lower bounds for mutual exclusion and other problems

  • Authors:
  • Hagit Attiya;Danny Hendler;Philipp Woelfel

  • Affiliations:
  • Technion, Haifa, Israel;Ben-Gurion University, Beer-Sheva, Israel;University of Calgary, Calgary, Canada

  • Venue:
  • STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
  • Year:
  • 2008

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Abstract

We investigate the remote memory references (RMRs) complexity of deterministic processes that communicate by reading and writing shared memory in asynchronous cache-coherent and distributed shared-memory multiprocessors. We define a class of algorithms that we call order encoding. By applying information-theoretic arguments, we prove that every order encoding algorithm, shared by n processes, has an execution that incurs Ω(n log n) RMRs. From this we derive the same lower bound for the mutual exclusion, bounded counter and store/collect synchronization problems. The bounds we obtain for these problems are tight. It follows from the results of [10] that our lower bounds hold also for algorithms that can use comparison primitives and load-linked/store-conditional in addition to reads and writes. Our mutual exclusion lower bound proves a longstanding conjecture of Anderson and Kim.