L1 pattern matching lower bound

Ohad Lipsky, Ely Porat

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish
Pages (from-to)141-143
Number of pages3
JournalInformation Processing Letters
Issue number4
StatePublished - 15 Feb 2008

Bibliographical note

Funding Information:
* Corresponding author. Tel.: +972 3 531 7620. E-mail addresses: ohadlipsky@yahoo.com (O. Lipsky), porately@cs.biu.ac.il (E. Porat). 1 Tel.: +972 3 531 8408. 2 Partially supported by GIF Young Scientists Program grant 2055-1168.6/2002.


  • Analysis of algorithms
  • Lower bound
  • Pattern matching
  • Time series analysis


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