NDLI: Gap Theorems for Distributed Computation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Warmuth, Manfred K. Moran, Shlomo
Copyright Year	1993
Abstract	Consider a bidirectional ring of n identical processors that communicate asynchronously. The processors have no identifiers, and hence the ring is called anonymous. Each processor receives an input letter, and the ring is to compute a function of the circular input string. If the function value is constant for all input strings, then the processors do not need to send any messages. On the other hand, it is proven that any deterministic algorithm that computes any nonconstant function for anonymous rings requires $\Omega (n\log n)$ bits of communication for some input string. Also exhibited are nonconstant functions that require $O(n\log n)$ bits of communication for every input string. The same gap for the bit complexity of nonconstant functions remains even if the processors have distinct identifiers, provided that the identifiers are taken from a large enough domain.When the communication is measured in messages rather than bits, the results change. A nonconstant function that can be computed with $O(n\log ^ * n)$ messages on an anonymous ring is presented.
Starting Page	379
Ending Page	394
Page Count	16
File Format	PDF
ISSN	00975397
DOI	10.1137/0222028
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	22
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	Modes of computation message complexity Analysis of algorithms and problem complexity ring of processors distributed algorithms asynchronous bit complexity Network design and communication networks lower bounds gap theorem Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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