# Compressed communication complexity of hamming distance

Shiori Mitsuya, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

2 被引用数 (Scopus)

## 抄録

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. 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.

本文言語 英語 116 Algorithms 14 4 https://doi.org/10.3390/a14040116 出版済み - 2021

## !!!All Science Journal Classification (ASJC) codes

• 理論的コンピュータサイエンス
• 数値解析
• 計算理論と計算数学
• 計算数学

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