Coding for locality in reconstructing permutations
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding approach. The former approach boils down to presenting large se...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2018
|
| Online Access: | http://hdl.handle.net/1721.1/114517 https://orcid.org/0000-0003-4059-407X |
| _version_ | 1826189800896462848 |
|---|---|
| author | Raviv, Netanel Yaakobi, Eitan Medard, Muriel |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Raviv, Netanel Yaakobi, Eitan Medard, Muriel |
| author_sort | Raviv, Netanel |
| collection | MIT |
| description | The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding approach. The former approach boils down to presenting large sets of permutations with locality, that is, any symbol of the permutation can be computed from a small set of other symbols. In the latter approach, a permutation may be coded in order to achieve locality. Both approaches must present low query complexity to allow the user to find an element efficiently. We discuss both approaches, and give a particular focus to the combinatorial one. In the combinatorial approach, we provide upper and lower bounds for the maximal size of a set of permutations with locality, and provide several simple constructions which attain the upper bound. In cases where the upper bound is not attained, we provide alternative constructions using a variety of tools, such as Reed-Solomon codes, permutation polynomials, and multi-permutations. In addition, several low-rate constructions of particular interest are discussed. In the coding approach we discuss an alternative representation of permutations, present a paradigm for supporting arbitrary powers of the stored permutation, and conclude with a proof of concept that permutations may be stored more efficiently than ordinary strings over the same alphabet. |
| first_indexed | 2024-09-23T08:22:30Z |
| format | Article |
| id | mit-1721.1/114517 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:22:30Z |
| publishDate | 2018 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1145172022-09-23T12:32:12Z Coding for locality in reconstructing permutations Raviv, Netanel Yaakobi, Eitan Medard, Muriel Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Medard, Muriel The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding approach. The former approach boils down to presenting large sets of permutations with locality, that is, any symbol of the permutation can be computed from a small set of other symbols. In the latter approach, a permutation may be coded in order to achieve locality. Both approaches must present low query complexity to allow the user to find an element efficiently. We discuss both approaches, and give a particular focus to the combinatorial one. In the combinatorial approach, we provide upper and lower bounds for the maximal size of a set of permutations with locality, and provide several simple constructions which attain the upper bound. In cases where the upper bound is not attained, we provide alternative constructions using a variety of tools, such as Reed-Solomon codes, permutation polynomials, and multi-permutations. In addition, several low-rate constructions of particular interest are discussed. In the coding approach we discuss an alternative representation of permutations, present a paradigm for supporting arbitrary powers of the stored permutation, and conclude with a proof of concept that permutations may be stored more efficiently than ordinary strings over the same alphabet. 2018-04-03T17:49:58Z 2018-05-06T05:00:05Z 2017-07 2017-06 2018-01-31T05:00:26Z Article http://purl.org/eprint/type/JournalArticle 0925-1022 1573-7586 http://hdl.handle.net/1721.1/114517 Raviv, Netanel, et al. “Coding for Locality in Reconstructing Permutations.” Designs, Codes and Cryptography, vol. 86, no. 2, Feb. 2018, pp. 387–418. https://orcid.org/0000-0003-4059-407X en http://dx.doi.org/10.1007/s10623-017-0378-9 Designs, Codes and Cryptography Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer Science+Business Media, LLC application/pdf Springer US Springer US |
| spellingShingle | Raviv, Netanel Yaakobi, Eitan Medard, Muriel Coding for locality in reconstructing permutations |
| title | Coding for locality in reconstructing permutations |
| title_full | Coding for locality in reconstructing permutations |
| title_fullStr | Coding for locality in reconstructing permutations |
| title_full_unstemmed | Coding for locality in reconstructing permutations |
| title_short | Coding for locality in reconstructing permutations |
| title_sort | coding for locality in reconstructing permutations |
| url | http://hdl.handle.net/1721.1/114517 https://orcid.org/0000-0003-4059-407X |
| work_keys_str_mv | AT ravivnetanel codingforlocalityinreconstructingpermutations AT yaakobieitan codingforlocalityinreconstructingpermutations AT medardmuriel codingforlocalityinreconstructingpermutations |