Abstract
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.
Original language | English |
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Article number | 7342968 |
Pages (from-to) | 703-712 |
Number of pages | 10 |
Journal | IEEE Transactions on Information Theory |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - 1 Feb 2016 |
Keywords
- Chebyshev metric
- Covering codes
- Kendall τ-metric
- Permutations
- Rank modulation
- Rate-distortion
- ℓ-metric
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences