Tournaments for mutual exclusion: verification and concurrent complexity

Tournaments for mutual exclusion: verification and concurrent complexity Given a mutual exclusion algorithm MXd for $${d \geq 2}$$ d ≥ 2 threads, a mutual exclusion algorithm for $${N > d}$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Formal Aspects of Computing Springer Journals

Tournaments for mutual exclusion: verification and concurrent complexity

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Publisher
Springer London
Copyright
Copyright © 2017 by The Author(s)
Subject
Computer Science; Math Applications in Computer Science; Theory of Computation; Computational Mathematics and Numerical Analysis
ISSN
0934-5043
eISSN
1433-299X
D.O.I.
10.1007/s00165-016-0407-x
Publisher site
See Article on Publisher Site

Abstract

Given a mutual exclusion algorithm MXd for $${d \geq 2}$$ d ≥ 2 threads, a mutual exclusion algorithm for $${N > d}$$ 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.

Journal

Formal Aspects of ComputingSpringer Journals

Published: Jan 27, 2017

References

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