English

Streaming k-mismatch with error correcting and applications

Data Structures and Algorithms 2019-04-24 v3

Abstract

We present a new streaming algorithm for the kk-Mismatch problem, one of the most basic problems in pattern matching. Given a pattern and a text, the task is to find all substrings of the text that are at the Hamming distance at most kk from the pattern. Our algorithm is enhanced with an important new feature called Error Correcting, and its complexities for k=1k=1 and for a general kk are comparable to those of the solutions for the kk-Mismatch problem by Porat and Porat (FOCS 2009) and Clifford et al. (SODA 2016). In parallel to our research, a yet more efficient algorithm for the kk-Mismatch problem with the Error Correcting feature was developed by Clifford et al. (SODA 2019). Using the new feature and recent work on streaming Multiple Pattern Matching we develop a series of streaming algorithms for pattern matching on weighted strings, which are a commonly used representation of uncertain sequences in molecular biology. We also show that these algorithms are space-optimal up to polylog factors. A preliminary version of this work was published at DCC 2017 conference.

Keywords

Cite

@article{arxiv.1607.05626,
  title  = {Streaming k-mismatch with error correcting and applications},
  author = {Jakub Radoszewski and Tatiana Starikovskaya},
  journal= {arXiv preprint arXiv:1607.05626},
  year   = {2019}
}
R2 v1 2026-06-22T14:58:38.475Z