NDLI: Function Matching

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Amir, Amihood Aumann, Yonatan Lewenstein, Moshe Porat, Ely
Copyright Year	2006
Abstract	We present problems in the following three application areas: identifying similar codes in which global register reallocation and spill code minimization were done (programming languages); protein threading (computational biology); and searching for color icons under different color maps (image processing).We introduce a new search model called function matching that enables us to solve the above problems. The function matching problem has as its input a text T of length n over alphabet $\Sigma_T$ and a pattern $P = P[1] P[2] \cdots P[m]$ of length m over alphabet $\Sigma_P$. We seek all text locations i, where the m-length substring that starts at i is equal to $f(P[1]) f(P[2]) \cdots f(P[m])$, for some function $f: \Sigma_P \rightarrow \Sigma_T$.We give a randomized algorithm that solves the function matching problem in time $O(n\log n)$ with probability ${1\over n}$ of declaring a false positive. We give a deterministic algorithm whose time is $O(n \|\Sigma_P\| \log m)$ and show that it is optimal in the convolutions model. We use function matching to efficiently solve the problem of two-dimensional parameterized matching.
Starting Page	1007
Ending Page	1022
Page Count	16
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539702424496
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Models of computation pattern matching Analysis of algorithms and problem complexity color maps parameterized matching function matching
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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