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Tournaments for mutual exclusion: verification and concurrent complexity

Formal Aspects of Computing volume 29, pages 833–852 (2017)Cite this article

Abstract

Given a mutual exclusion algorithm MXd for \({d \geq 2}\) threads, a mutual exclusion algorithm for \({N > d}\) threads can be built in a tree of degree d with N leaves, with the critical section at the root of the tree. This tournament solution seems obviously correct and efficient. The present note proves the correctness, and formalizes the efficiency in terms of concurrent complexity by means of Bounded Unity. If the tree is balanced, the throughput is logarithmic in N. If moreover MXd satisfies FCFS (first-come first-served), the worst case individual delay of the tournament algorithm is of order N. This is optimal.

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  1. Johann Bernoulli Institute for Mathematics and Computer Science University of Groningen, P.O.Box 407, 9700 AK, Groningen, The Netherlands

    Wim H. Hesselink

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  1. Wim H. Hesselink
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Correspondence to Wim H. Hesselink.

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Xinyu Feng

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Hesselink, W.H. Tournaments for mutual exclusion: verification and concurrent complexity. Form Asp Comp 29, 833–852 (2017). https://doi.org/10.1007/s00165-016-0407-x

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  • DOI: https://doi.org/10.1007/s00165-016-0407-x

Keywords

  • Mutual exclusion
  • unity
  • Concurrency
  • Shared variables
  • Concurrent complexity