Compressed Communication Complexity of Hamming Distance
We consider the communication complexity of the <i>Hamming distance</i> of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their strings in a compressed form, i.e., represe...
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doaj-db6c16b05738454b8ea4d7c18cf54d852021-04-03T23:02:00ZengMDPI AGAlgorithms1999-48932021-04-011411611610.3390/a14040116Compressed Communication Complexity of Hamming DistanceShiori Mitsuya0Yuto Nakashima1Shunsuke Inenaga2Hideo Bannai3Masayuki Takeda4Department of Informatics, Kyushu University, 744, Motooka, Nishiku, Fukuoka 819-0395, JapanDepartment of Informatics, Kyushu University, 744, Motooka, Nishiku, Fukuoka 819-0395, JapanDepartment of Informatics, Kyushu University, 744, Motooka, Nishiku, Fukuoka 819-0395, JapanM&D Data Science Center, Tokyo Medical and Dental University, Tokyo 101-0062, JapanDepartment of Informatics, Kyushu University, 744, Motooka, Nishiku, Fukuoka 819-0395, JapanWe consider the communication complexity of the <i>Hamming distance</i> of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their strings in a compressed form, i.e., represented by the Lempel-Ziv 77 factorization (LZ77) with/without self-references. We present a randomized public-coin protocol for a joint computation of the Hamming distance of two strings represented by LZ77 without self-references. Although our scheme is heavily based on Bille et al.’s LCP protocol, our complexity analysis is original which uses Crochemore’s C-factorization and Rytter’s AVL-grammar. As a byproduct, we also show that LZ77 with/without self-references are not monotonic in the sense that their sizes can increase by a factor of 4/3 when a prefix of the string is removed.https://www.mdpi.com/1999-4893/14/4/116communication complexityHamming distanceLempel-Ziv compression |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shiori Mitsuya Yuto Nakashima Shunsuke Inenaga Hideo Bannai Masayuki Takeda |
spellingShingle |
Shiori Mitsuya Yuto Nakashima Shunsuke Inenaga Hideo Bannai Masayuki Takeda Compressed Communication Complexity of Hamming Distance Algorithms communication complexity Hamming distance Lempel-Ziv compression |
author_facet |
Shiori Mitsuya Yuto Nakashima Shunsuke Inenaga Hideo Bannai Masayuki Takeda |
author_sort |
Shiori Mitsuya |
title |
Compressed Communication Complexity of Hamming Distance |
title_short |
Compressed Communication Complexity of Hamming Distance |
title_full |
Compressed Communication Complexity of Hamming Distance |
title_fullStr |
Compressed Communication Complexity of Hamming Distance |
title_full_unstemmed |
Compressed Communication Complexity of Hamming Distance |
title_sort |
compressed communication complexity of hamming distance |
publisher |
MDPI AG |
series |
Algorithms |
issn |
1999-4893 |
publishDate |
2021-04-01 |
description |
We consider the communication complexity of the <i>Hamming distance</i> of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their strings in a compressed form, i.e., represented by the Lempel-Ziv 77 factorization (LZ77) with/without self-references. We present a randomized public-coin protocol for a joint computation of the Hamming distance of two strings represented by LZ77 without self-references. Although our scheme is heavily based on Bille et al.’s LCP protocol, our complexity analysis is original which uses Crochemore’s C-factorization and Rytter’s AVL-grammar. As a byproduct, we also show that LZ77 with/without self-references are not monotonic in the sense that their sizes can increase by a factor of 4/3 when a prefix of the string is removed. |
topic |
communication complexity Hamming distance Lempel-Ziv compression |
url |
https://www.mdpi.com/1999-4893/14/4/116 |
work_keys_str_mv |
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