Compressed communication complexity of hamming distance

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number116
Issue number4
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Computational Mathematics


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