The probabilistic method yields deterministic parallel algorithms
Rajeev Motwani,Joseph (Seffi) Naor,Moni Naor +2 more
- Vol. 49, Iss: 3, pp 478-516
Reads0
Chats0
TLDR
The general form of the case for which the method of conditional probabilities can be applied in the parallel context is given and the reason why this form does not lend itself to parallelization is discussed.Abstract:
A method is provided for converting randomized parallel algorithms into deterministic parallel algorithms. The approach is based on a parallel implementation of the method of conditional probabilities. Results obtained by applying the method to the set balancing problem, lattice approximation, edge-coloring graphs, random sampling, and combinatorial constructions are presented. The general form in which the method of conditional probabilities is applied sequentially is described. The reason why this form does not lend itself to parallelization are discussed. The general form of the case for which the method of conditional probabilities can be applied in the parallel context is given. >read more
Citations
More filters
Randomized Algorithms
TL;DR: For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. as discussed by the authors introduces the basic concepts in the design and analysis of randomized algorithms and provides a comprehensive and representative selection of the algorithms that might be used in each of these areas.
Journal ArticleDOI
Randomness is Linear in Space
Noam Nisan,David Zuckerman +1 more
TL;DR: In this article, it was shown that any randomized algorithm that runs in spaceSand timeT and uses poly(S) random bits can be simulated using only O(S ) random bits in space Sand timeT+poly(S).
Proceedings Article
Randomness is linear in space
Noam Nisan,David Zuckerman +1 more
TL;DR: Of independent interest is the main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.
Proceedings ArticleDOI
Splitters and near-optimal derandomization
TL;DR: A fairly general method for finding deterministic constructions obeying k-restrictions, which yields structures of size not much larger than the probabilistic bound and imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal /spl Sigma/II/Spl Sigma/ threshold formulae.
Proceedings ArticleDOI
Chernoff-Hoeffding bounds for applications with limited independence
TL;DR: The limited independence result implies that a reduced amount and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the CH bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routing.
References
More filters
Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Journal ArticleDOI
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Journal ArticleDOI
The NP-Completeness of Edge-Coloring
TL;DR: It is shown that it is NP-complete to determine the chromatic index of an arbitrary graph, even for cubic graphs.
Journal ArticleDOI
On the ratio of optimal integral and fractional covers
TL;DR: It is shown that the ratio of optimal integral and fractional covers of a hypergraph does not exceed 1 + log d, where d is the maximum degree and this theorem may replace probabilistic methods in certain circumstances.
Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.