Faster Approximate Pattern Matching in Compressed Repetitive Texts
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by
Travis Gagie and Paweł Gawrychowski and Christopher Hoobin and
Simon J. Puglisi
2012
Abstract
Motivated by the imminent growth of massive, highly redundant genomic
databases, we study the problem of compressing a string database while
simultaneously supporting fast random access, substring extraction and pattern
matching to the underlying string(s). Bille et al. (2011) recently showed how,
given a straight-line program with r rules for a string s of length n, we
can build an r-word data structure that allows us to extract any
substring of length m in n + m time. They also showed how, given
a pattern p of length m and an edit distance (k ≤ m), their data
structure supports finding all approximate matches to p in s in r
( (m k, k^4 + m) + n) + time. Rytter (2003) and Charikar et al.
(2005) showed that r is always at least the number z of phrases in the LZ77
parse of s, and gave algorithms for building straight-line programs with
z n rules. In this paper we give a simple z n-word data
structure that takes the same time for substring extraction but only z
(m k, k^4 + m) + time for approximate pattern matching.
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