TY - JOUR

T1 - Randomized mutual exclusion with sub-logarithmic RMR-complexity

AU - Hendler, Danny

AU - Woelfel, Philipp

N1 - Funding Information:
P. Woelfel was supported by NSERC.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. Attiya, Hendler, and Woelfel (40th STOC, 2008) established an Ω(log N) lower bound on the number of RMRs incurred by processes as they enter and exit the critical section, where N is the number of processes in the system. This matches the upper bound of Yang and Anderson (Distrib. Comput. 9(1):51-60, 1995). The upper and lower bounds apply for algorithms that only use read and write operations. The lower bound of Attiya et al.; however, only holds for deterministic algorithms. The question of whether randomized mutual exclusion algorithms, using reads and writes only, can achieve sub-logarithmic expected RMR complexity remained open. We answer this question in the affirmative by presenting starvation-free randomized mutual exclusion algorithms for the cache coherent (CC) and the distributed shared memory (DSM) model that have sub-logarithmic expected RMR complexity against the strong adversary. More specifically, each process incurs an expected number of O(log N / log log N) RMRs per passage through the entry and exit sections, while in the worst case the number of RMRs is O(log N).

AB - Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. Attiya, Hendler, and Woelfel (40th STOC, 2008) established an Ω(log N) lower bound on the number of RMRs incurred by processes as they enter and exit the critical section, where N is the number of processes in the system. This matches the upper bound of Yang and Anderson (Distrib. Comput. 9(1):51-60, 1995). The upper and lower bounds apply for algorithms that only use read and write operations. The lower bound of Attiya et al.; however, only holds for deterministic algorithms. The question of whether randomized mutual exclusion algorithms, using reads and writes only, can achieve sub-logarithmic expected RMR complexity remained open. We answer this question in the affirmative by presenting starvation-free randomized mutual exclusion algorithms for the cache coherent (CC) and the distributed shared memory (DSM) model that have sub-logarithmic expected RMR complexity against the strong adversary. More specifically, each process incurs an expected number of O(log N / log log N) RMRs per passage through the entry and exit sections, while in the worst case the number of RMRs is O(log N).

KW - Mutual exclusion

KW - RMRs

KW - Randomization

KW - Remote memory references

KW - Strong adversary

UR - http://www.scopus.com/inward/record.url?scp=85027954064&partnerID=8YFLogxK

U2 - 10.1007/s00446-011-0128-6

DO - 10.1007/s00446-011-0128-6

M3 - Article

AN - SCOPUS:85027954064

VL - 24

SP - 3

EP - 19

JO - Distributed Computing

JF - Distributed Computing

SN - 0178-2770

IS - 1

ER -