 
Summary: Real Scaled Matching
Amihood Amir \Lambday Ayelet Butman \Lambda Moshe Lewenstein \Lambda z
BarIlan University BarIlan University BarIlan University
and
Georgia Tech
Abstract
Scaled Matching refers to the problem of finding all locations in the text where
the pattern, proportionally enlarged according to an arbitrary integral scale, appears.
Scaled matching is an important problem that was originally inspired by problems in
Vision.
However, in real life, a more natural model of scaled matching is the Real Scaled
Matching model. Real scaled matching is an extended version of the scaled match
ing problem allowing arbitrary realsized scales, approximated by some function, e.g.
truncation.
It has been shown that the scaled matching problem can be solved in linear time.
However, even though there has been followup work on the problem, it remained an
open question whether real scaled matching could be solved faster than the simple
solution of O(nm) time, where n is the text size and m is the pattern size.
Using a new approach we show how to solve the real scaled matching problem in
linear time.
