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

Moshe Schwartz; Pascal O. Vontobel

doi: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

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

1 Scopus citations

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	English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers
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	2015 IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, China Duration: 14 Jun 2015 → 19 Jun 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Conference

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

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2015.7282752

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Schwartz, M., & Vontobel, P. O. (2015). Bounds on the size of balls over permutations with the infinity metric. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1731-1735). Article 7282752 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2015.7282752

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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.",

author = "Moshe Schwartz and Vontobel, \{Pascal O.\}",

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year = "2015",

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doi = "10.1109/ISIT.2015.7282752",

language = "English",

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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, Institute of Electrical and Electronics Engineers, pp. 1731-1735, 2015 IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, China, 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. Institute of Electrical and Electronics Engineers, 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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