Summary: Overlap Matching
Amihood Amir \Lambda Richard Cole y Ramesh Hariharan z
Bar­Ilan University & Georgia Tech New York University Indian Institute of Science
Moshe Lewenstein x Ely Porat --
Bar­Ilan University Bar­Ilan University & Weizmann Institute
Abstract
We propose a new paradigm for string matching, namely structural matching. In structural
matching, the text and pattern contents are not important. Rather, some areas in the text and
patterns are singled out, say intervals. A ``match'' is a text location where a specified relation
between the text and pattern areas is satisfied.
In particular we define the structural matching problem of Overlap (Parity) Matching. We
seek the text locations where all overlaps of the given pattern and text intervals have even
length. We show that this problem can be solved in time O(n log m), where the text length is
n and the pattern length is m.
As an application of overlap matching, we show how to reduce the String Matching with
Swaps problem to the overlap matching problem. The String Matching with Swaps problem is
the problem of string matching in the presence of local swaps. The best known deterministic
upper bound for this problem was O(nm 1=3 log m log oe) for a general alphabet \Sigma, where oe =
min(m; j\Sigmaj).
Our reduction provides a solution to the pattern matching with swaps problem in time

Source: Amir, Amihood - Computer Science Department, Bar Ilan University
Mohri, Mehryar - Computer Science Department, Courant Institute of Mathematical Sciences, New York University
Porat, Ely - Computer Science Department, Bar Ilan University

Collections: Computer Technologies and Information Sciences; Mathematics