NDLI: A Time-Randomness Trade-Off for Oblivious Routing

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Upfal, Eli Peleg, David
Copyright Year	1990
Abstract	Three parameters characterize the performance of a probabilistic algorithm: T, the run-time 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. A tight trade-off between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks is presented. 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 $1 - Q$ is proved. It is shown that this lower bound is almost optimal by proving the existence, for every $e^{3} \log N \leqq T \leqq N^{{1 / 2}}$, of an oblivious algorithm that terminates in T steps with probability $1 - Q$ and uses $(1- Q + o(1)) \log ({N / T}) - \log Q$ independent random bits. This result is complemented 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.
Starting Page	256
Ending Page	266
Page Count	11
File Format	PDF
ISSN	00975397
DOI	10.1137/0219017
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	resource trade-off permutation routing Analysis of algorithms and problem complexity communication networks randomized algorithms Network design and communication Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in