Compressed Communication Complexity of Hamming Distance [article]

Shiori Mitsuya, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
2021 arXiv   pre-print
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
more » ... eferences. 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.
arXiv:2103.03468v2 fatcat:k5xitiu7a5gl3m47nv62fxo53y