2021/03/05 by Shiori Mitsuya, Yuto Nakashima, Mitsuya, Shiori +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Computational Complexity (cs.CC) #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2103.03468
openalex publication_date 2021/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.