Function matching: Algorithms, applications, and a lower bound

A. Amihood, Y Aumann, R Cole, M Lewenstein, E Porat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 publicationInternational Colloquium on Automata, Languages, and Programming
EditorsJos C. M. Baeten, Jan Karel Lenstra, Joachim Parrow, Gerhard J. Woeginger, Jan Karel, Lenstra Joachim, Parrow Gerhard, J. Woeginger
PublisherSpringer Berlin Heidelberg
StatePublished - 2003

Bibliographical note

Place of conference:The Netherlands


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