Approximate matching in the L1 metric

Amihood Amir, Ohad Lipsky, Ely Porat, Julia Umanski

Research output: Contribution to journalConference articlepeer-review

28 Scopus citations


Approximate matching is one of the fundamental problems in pattern matching, and a ubiquitous problem in real applications. The Hamming distance is a simple and well studied example of approximate matching, motivated by typing, or noisy channels. Biological and image processing applications assign a different value to mismatches of different symbols. We consider the problem of approximate matching in the L1 metric - the k-L1-distance problem. Given text T = to, ..., tn-1 and pattern P = po, ..., pm-1 strings of natural number, and a natural number k, we seek all text locations i where the L1 distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. ∑j=0m-1 |ti+j-pj| ≤ k. We provide an algorithm that solves the k-L1 -distance problem in time O(n √k log k). The algorithm applies a bounded divide-and-conquer approach and makes noveluses of non-boolean convolutions.

Original languageEnglish
Pages (from-to)91-103
Number of pages13
JournalLecture Notes in Computer Science
StatePublished - 2005
EventOt16th Annual Symposium on Combinatorial Pattern Matching, CPM 2005 - Jeju Island, Korea, Republic of
Duration: 19 Jun 200522 Jun 2005


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