Improved upper bounds for random-edge and random-jump on abstract cubes

Thomas Dueholm Hansen; Mike Paterson; Uri Zwick

doi:10.1137/1.9781611973402.65

Improved upper bounds for random-edge and random-jump on abstract cubes

Thomas Dueholm Hansen, Mike Paterson, Uri Zwick

School of Computer Science

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

12 Scopus citations

Abstract

Upper bounds are given for the complexity of two very natural randomized algorithms for finding the sink of an Acyclic Unique Sink Orientation (AUSO) of the n-cube. For Random-Edge, we obtain an upper bound of about 1.80ⁿ, improving upon the the previous upper bound of about 2ⁿ/n ^logn obtained by Gartner and Kaibel. For Random- Jump, we obtain an upper bound of about (3/2)ⁿ, improving upon the previous upper bound of about 1.72ⁿ obtained by Mansour and Singh. AUSOs provide an appealing combinatorial abstraction of linear programming and other computational problems such as finding optimal strategies for turn-based Stochastic Games.

Original language	English
Title of host publication	Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Publisher	Association for Computing Machinery
Pages	874-881
Number of pages	8
ISBN (Print)	9781611973389
DOIs	https://doi.org/10.1137/1.9781611973402.65
State	Published - 2014
Event	25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States Duration: 5 Jan 2014 → 7 Jan 2014

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference	25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Country/Territory	United States
City	Portland, OR
Period	5/01/14 → 7/01/14

Funding

Funders	Funder number
Bloom's Syndrome Foundation	2012338
Engineering and Physical Sciences Research Council
Engineering and Physical Sciences Research Council	EP/D063191/1

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10.1137/1.9781611973402.65

Cite this

Hansen, T. D., Paterson, M., & Zwick, U. (2014). Improved upper bounds for random-edge and random-jump on abstract cubes. In Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 (pp. 874-881). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973402.65

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title = "Improved upper bounds for random-edge and random-jump on abstract cubes",

abstract = "Upper bounds are given for the complexity of two very natural randomized algorithms for finding the sink of an Acyclic Unique Sink Orientation (AUSO) of the n-cube. For Random-Edge, we obtain an upper bound of about 1.80n, improving upon the the previous upper bound of about 2n/n logn obtained by Gartner and Kaibel. For Random- Jump, we obtain an upper bound of about (3/2)n, improving upon the previous upper bound of about 1.72n obtained by Mansour and Singh. AUSOs provide an appealing combinatorial abstraction of linear programming and other computational problems such as finding optimal strategies for turn-based Stochastic Games.",

author = "Hansen, {Thomas Dueholm} and Mike Paterson and Uri Zwick",

year = "2014",

doi = "10.1137/1.9781611973402.65",

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publisher = "Association for Computing Machinery",

pages = "874--881",

booktitle = "Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014",

note = "25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 ; Conference date: 05-01-2014 Through 07-01-2014",

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Hansen, TD, Paterson, M & Zwick, U 2014, Improved upper bounds for random-edge and random-jump on abstract cubes. in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 874-881, 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, OR, United States, 5/01/14. https://doi.org/10.1137/1.9781611973402.65

Improved upper bounds for random-edge and random-jump on abstract cubes. / Hansen, Thomas Dueholm; Paterson, Mike; Zwick, Uri.
Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, 2014. p. 874-881 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

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

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Improved upper bounds for random-edge and random-jump on abstract cubes

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