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.
@InProceedings{clifford_et_al:DagSemProc.09281.5, 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 = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.5}, URN = {urn:nbn:de:0030-drops-22442}, doi = {10.4230/DagSemProc.09281.5}, annote = {Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching} }
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