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Streaming Dictionary Matching with Mismatches

Authors Paweł Gawrychowski, Tatiana Starikovskaya

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Author Details

Paweł Gawrychowski
  • University of Wrocław, 50-137 Wrocław, Poland
Tatiana Starikovskaya
  • DIENS, École normale supérieure, PSL Research University, 75005 Paris, France

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving this paper.

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Paweł Gawrychowski and Tatiana Starikovskaya. Streaming Dictionary Matching with Mismatches. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CPM.2019.21

Abstract

In the k-mismatch problem we are given a pattern of length m and a text and must find all locations where the Hamming distance between the pattern and the text is at most k. A series of recent breakthroughs have resulted in an ultra-efficient streaming algorithm for this problem that requires only O(k log m/k) space [Clifford, Kociumaka, Porat, SODA 2019]. In this work, we consider a strictly harder problem called dictionary matching with k mismatches, where we are given a dictionary of d patterns of lengths at most m and must find all their k-mismatch occurrences in the text, and show the first streaming algorithm for it. The algorithm uses O(k d log^k d polylog m) space and processes each position of the text in O(k log^k d polylog m + occ) time, where occ is the number of k-mismatch occurrences of the patterns that end at this position. The algorithm is randomised and outputs correct answers with high probability.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Streaming
  • multiple pattern matching
  • Hamming distance

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