License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.09281.5
URN: urn:nbn:de:0030-drops-22442
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Clifford, Raphael ; Efremo, Klim ; Porat, Ely ; Rotschild, Amir

Pattern matching with don't cares and few errors

09281.PoratEly.Paper.2244.pdf (0.3 MB)


We present solutions for the k-mismatch pattern matching problem
with don't cares. Given a text t of length n and a pattern p of length m
with don't care symbols and a bound k, our algorithms find all the places
that the pattern matches the text with at most k mismatches. We first
give an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds
the correct answer with high probability. We then present a new deter-
ministic \Theta(nk^2 log^m)time solution that uses tools originally developed
for group testing. Taking our derandomisation approach further we de-
velop an approach based on k-selectors that runs in \Theta(nk polylogm) time.
Further, in each case the location of the mismatches at each alignment is
also given at no extra cost.

BibTeX - Entry

  author =	{Clifford, Raphael and Efremo, Klim and Porat, Ely and Rotschild, Amir},
  title =	{{Pattern matching with don't cares and few errors}},
  booktitle =	{Search Methodologies},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-22442},
  doi =		{10.4230/DagSemProc.09281.5},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}

Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching
Collection: 09281 - Search Methodologies
Issue Date: 2009
Date of publication: 10.11.2009

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