Bounds on the size of balls over permutations with the infinity metric

Moshe Schwartz; Pascal O. Vontobel

doi:https://doi.org/10.1109/ISIT.2015.7282752

Bounds on the size of balls over permutations with the infinity metric

Moshe Schwartz, Pascal O. Vontobel

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

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

Abstract

We study the size (or volume) of balls in the metric space of permutations, S_n, under the infinity metric. We focus on the regime of balls with radius r = ρ (n-1), ρ [0, 1], i.e., a radius that is a constant fraction of the maximum possible distance. We provide new bounds on the size of such balls. These bounds reduce the asymptotic gap between the upper and lower bound to at most 0.06 bits per symbol.

Original language	American English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Pages	1731-1735
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282752
State	Published - 28 Sep 2015
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June

Conference

Conference	IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	Hong Kong
City	Hong Kong
Period	14/06/15 → 19/06/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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https://doi.org/10.1109/ISIT.2015.7282752

Cite this

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title = "Bounds on the size of balls over permutations with the infinity metric",

abstract = "We study the size (or volume) of balls in the metric space of permutations, Sn, under the infinity metric. We focus on the regime of balls with radius r = ρ (n-1), ρ [0, 1], i.e., a radius that is a constant fraction of the maximum possible distance. We provide new bounds on the size of such balls. These bounds reduce the asymptotic gap between the upper and lower bound to at most 0.06 bits per symbol.",

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Schwartz, M & Vontobel, PO 2015, Bounds on the size of balls over permutations with the infinity metric. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282752, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, pp. 1731-1735, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 14/06/15. https://doi.org/10.1109/ISIT.2015.7282752

Bounds on the size of balls over permutations with the infinity metric. / Schwartz, Moshe; Vontobel, Pascal O.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. 2015. p. 1731-1735 7282752 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

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

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AB - We study the size (or volume) of balls in the metric space of permutations, Sn, under the infinity metric. We focus on the regime of balls with radius r = ρ (n-1), ρ [0, 1], i.e., a radius that is a constant fraction of the maximum possible distance. We provide new bounds on the size of such balls. These bounds reduce the asymptotic gap between the upper and lower bound to at most 0.06 bits per symbol.

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Bounds on the size of balls over permutations with the infinity metric

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