Bounds for Permutation Rate-Distortion

Bounds for Permutation Rate-Distortion

We study the rate-distortion relationship in the set of permutations endowed with the Kendall τ-metric and the Chebyshev metric (the ℓ ∞ -metric). This paper is motivated by the application of permutation rate-distortion to the average-case and worst-case distortion analysis of algorithms for rankin...

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Veröffentlicht in:IEEE transactions on information theory 2016-02, Vol.62 (2), p.703-712
Hauptverfasser: Hassanzadeh, Farzad Farnoud, Schwartz, Moshe, Bruck, Jehoshua
Format: Artikel
Sprache:eng
Schlagworte:
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <inline-formula> <tex-math notation="LaTeX"> {\ell _\infty} </tex-math> </inline-formula> -metric
Algorithm design and analysis
Algorithms
Approximation
Approximation algorithms
Chebyshev approximation
Chebyshev metric
Codes
Construction
covering codes
Distortion
Error correction codes
Information theory
Kendall <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <inline-formula> <tex-math notation="LaTeX"> tau </tex-math> </inline-formula> -metric
Measurement
Metric system
Permutations
Rank modulation
Rate-distortion
Sorting algorithms
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Beschreibung
Zusammenfassung:We study the rate-distortion relationship in the set of permutations endowed with the Kendall τ-metric and the Chebyshev metric (the ℓ ∞ -metric). This paper is motivated by the application of permutation rate-distortion to the average-case and worst-case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall τ-metric, we provide bounds for various distortion regimes, while for the Chebyshev metric, we present bounds that are valid for all distortions and are especially accurate for small distortions. In addition, for the Chebyshev metric, we provide a construction for covering codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2504521