NDLI: Time and Space Lower Bounds for Nonblocking Implementations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tan, King Jayanti, Prasad Toueg, Sam
Copyright Year	2000
Abstract	We show the following time and space complexity lower bounds. Let $\cal{I}$ be any randomized nonblocking n-process implementation of any object in set A from any combination of objects in set B, where A = {increment, fetch&add, modulo k counter (for any $k \ge 2n$), LL/SC bit, k-valued compare&swap (for any $k \ge n$), single-writer snapshot}, and B = {resettable consensus} $\cup$ {historyless objects such as registers and swap registers}. The space complexity of $\cal{I}$ is at least n-1. Moreover, if $\cal{I}$ is deterministic, both its time and space complexity are at least n-1. These lower bounds hold even if objects used in the implementation are of unbounded size.This improves on some of the $\Omega(\sqrt{n})$ space complexity lower bounds of Fich, Herlihy, and Shavit [i Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing, Ithaca, NY, 1993, pp. 241--249; J. Assoc. Comput. Mach., 45 (1998), pp. 843--862]. It also shows the near optimality of some known wait-free implementations in terms of space complexity.
Starting Page	438
Ending Page	456
Page Count	19
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539797317299
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	30
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Computational difficulty of problems nonblocking wait-free randomized shared object implementations time complexity synchronization asynchronous shared memory algorithms Distributed algorithms space complexity lower bounds
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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