Derandomization of euclidean random walks

Ilia Binder; Mark Braverman

doi:10.1007/978-3-540-74208-1_26

Derandomization of euclidean random walks

Ilia Binder, Mark Braverman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

7 Scopus citations

Abstract

We consider the problem of derandomizing random walks in the Euclidean space ℝ^k. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √log log n), where 1/n is the desired precision of the simulation.

Original language	English (US)
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Publisher	Springer Verlag
Pages	353-365
Number of pages	13
ISBN (Print)	9783540742074
DOIs	https://doi.org/10.1007/978-3-540-74208-1_26
State	Published - 2007
Externally published	Yes
Event	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States Duration: Aug 20 2007 → Aug 22 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4627 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Country/Territory	United States
City	Princeton, NJ
Period	8/20/07 → 8/22/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-74208-1_26

Cite this

Binder, I., & Braverman, M. (2007). Derandomization of euclidean random walks. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (pp. 353-365). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_26

Binder, Ilia ; Braverman, Mark. / Derandomization of euclidean random walks. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. pp. 353-365 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Derandomization of euclidean random walks",

abstract = "We consider the problem of derandomizing random walks in the Euclidean space ℝk. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √log log n), where 1/n is the desired precision of the simulation.",

author = "Ilia Binder and Mark Braverman",

note = "Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 ; Conference date: 20-08-2007 Through 22-08-2007",

year = "2007",

doi = "10.1007/978-3-540-74208-1_26",

language = "English (US)",

isbn = "9783540742074",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Binder, I & Braverman, M 2007, Derandomization of euclidean random walks. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, Springer Verlag, pp. 353-365, 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007, Princeton, NJ, United States, 8/20/07. https://doi.org/10.1007/978-3-540-74208-1_26

Derandomization of euclidean random walks. / Binder, Ilia; Braverman, Mark.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. p. 353-365 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Braverman, Mark

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N2 - We consider the problem of derandomizing random walks in the Euclidean space ℝk. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √log log n), where 1/n is the desired precision of the simulation.

AB - We consider the problem of derandomizing random walks in the Euclidean space ℝk. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √log log n), where 1/n is the desired precision of the simulation.

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DO - 10.1007/978-3-540-74208-1_26

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Approximation, Randomization, and Combinatorial Optimization

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Binder I, Braverman M. Derandomization of euclidean random walks. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag. 2007. p. 353-365. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74208-1_26

Derandomization of euclidean random walks

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