Compressed Communication Complexity of Hamming Distance
Abstract
We consider the communication complexity of the Hamming distance 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. While 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.
Keywords
Cite
@article{arxiv.2103.03468,
title = {Compressed Communication Complexity of Hamming Distance},
author = {Shiori Mitsuya and Yuto Nakashima and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
journal= {arXiv preprint arXiv:2103.03468},
year = {2021}
}