A time-randomness tradeoff for oblivious routing

Danny Krizanc, David Peleg, Eli Upfal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

26 Scopus citations

Abstract

Three parameters characterize the performance of a probabilistic algorithm: T, the runtime of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps and R, the amount of randomness used by the algorithm, measured by the entropy of its random source. We present a tight tradeoff between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks. We prove a (1 - Q) log N/T - log Q - O(1) lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q. We show that this lower bound is almost optimal by proving the existence, for every e3 log N ≤ T ≤ N1/2 an oblivious algorithm that terminates in T steps with probability 1 - Q and uses (l-Q+o(1))log N/T-log Q, independent random bits. We complement this result with an explicit construction of a family of oblivious algorithms that use less than a factor of log N more random bits than the optimal algorithm achieving the same run-time.

Original languageEnglish
Title of host publicationProceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC 1988
PublisherAssociation for Computing Machinery
Pages93-102
Number of pages10
ISBN (Print)0897912640, 9780897912648
DOIs
StatePublished - 1988
Externally publishedYes
Event20th Annual ACM Symposium on Theory of Computing, STOC 1988 - Chicago, IL, United States
Duration: 2 May 19884 May 1988

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference20th Annual ACM Symposium on Theory of Computing, STOC 1988
Country/TerritoryUnited States
CityChicago, IL
Period2/05/884/05/88

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