Compression in the Space of Permutations
Name
Wornell_Compression in.pdf
Size
438.79 KB
Format
Adobe PDF
Checksum (MD5)
031e2f08bcc9e9865fd2326dd33779ed
Author(s)
Mazumdar, Arya
Wang, Da
Wornell, Gregory W
Date Issued
December 2015
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Wang, Da et al. “Compression in the Space of Permutations.” IEEE Transactions on Information Theory 61, 12 (December 2015): 6417–6431 © 2015 Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion characteristic for the permutation space under the uniform distribution, and the minimum achievable rate of compression that allows a bounded distortion after recovery. Our analysis is with respect to different practical and useful distortion measures, including Kendall tau distance, Spearman's footrule, Chebyshev distance, and inversion-ℓ1 distance. We establish equivalence of source code designs under certain distortions and show simple explicit code designs that incur low encoding/decoding complexities and are asymptotically optimal. Finally, we show that for the Mallows model, a popular nonuniform ranking model on the permutation space, both the entropy and the maximum distortion at zero rate are much lower than the uniform counterparts, which motivates the future design of efficient compression schemes for this model.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tit.2015.2485270
