Alphabet Dependence in Parameterized Matching

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Title: Alphabet Dependence in Parameterized Matching
Author: Amir, Amihood ; Farach-Colton, Martin ; Muthukrishnan, S.
Abstract: The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set ∑. A recently introduced model is that of parameterized pattern matching; the main motivation for this scheme lies in software maintenance where programs are considered "identical" even if variables are different. Strings, under this model, additionally have symbols from a variable set Π and occurrences of one string in the other up to a renaming of the variables are sought. In this paper we show that finding the occurrences of a m-length string in a n-length string under the parameterized pattern matching paradigm can be done in time O (n log π), where π = min (m, ∣Π∣); that is , independent of ∣∑∣. Additionally, we show that in general this dependence on ∣Π∣ is inherent to any algorithm for this problem in the comparison model – that is, our algorithm is optimal.
Type: Technical Report
Date: 1993
Relation: CC Technical Report; GIT-CC-93-44
Publisher: Georgia Institute of Technology
Subject: Parameterized matching
Alphabet sets
Comparison models
Standard string matching

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