Function Matching: Algorithms, Applications and a Lower Bound

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Abstract

We introduce a new matching criterion — function matching — that captures several different applications. The function matching. problem has as its input a text T of length n over alphabet Σ T and a pattern P = P[1]P[2] ... P[m] of length m over alphabet Σ T. We seek all text locations i for which, for some function f: Σ T → Σ T (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2]) ... f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1nk1nk of declaring a false positive.W e give a deterministic algorithm whose time is O(n|Σ T| logm) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.
Original languageAmerican English
Title of host publication30th International Colloquium on Automata, Languages and Programming, (ICALP),
PublisherSpringer Berlin Heidelberg
StatePublished - 2003

Bibliographical note

Place of conference:Eindhoven, The Netherlands

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