Abstract
Let a text string T = t0, ..., tn - 1 and a pattern string P = p0, ..., pm - 1, ti, pj ∈ N be given. In the Approximate Pattern Matching in theL1 metric problem (L1-matching for short) the output is, for every text location i, the L1 distance between the pattern and the length m substring of the text starting at i, i.e. ∑j = 0m - 1 | ti + j - pj |. The Less Than Matching problem is that of finding all locations i of T where ti + j ≥ pj, j = 0, ..., m - 1. The String Matching with Mismatches problem is that of finding the number of mismatches between the pattern and every length m substring of the text. For the three above problems, the fastest known deterministic solution is O (n sqrt(m log m)) time. In this paper we show that the latter two problems can be linearly reduced to the problem of L1-matching.
Original language | English |
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Pages (from-to) | 141-143 |
Number of pages | 3 |
Journal | Information Processing Letters |
Volume | 105 |
Issue number | 4 |
DOIs | |
State | Published - 15 Feb 2008 |
Bibliographical note
Funding Information:* Corresponding author. Tel.: +972 3 531 7620. E-mail addresses: [email protected] (O. Lipsky), [email protected] (E. Porat). 1 Tel.: +972 3 531 8408. 2 Partially supported by GIF Young Scientists Program grant 2055-1168.6/2002.
Keywords
- Analysis of algorithms
- Lower bound
- Pattern matching
- Time series analysis