### Function Matching: Algorithms, Applications, and a Lower Bound [chapter]

Amihood Amir, Yonatan Aumann, Richard Cole, Moshe Lewenstein, Ely Porat
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
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 ΣT and a pattern P = P [1]P [2] · · · P [m] of length m over alphabet ΣP . We seek all text locations i for which, for some function f : ΣP → ΣT (f may also depend on i), the m-length substring that starts at i is equal to We give a randomized algorithm which, for any given constant k, solves the function
more &raquo; ... g problem in time O(n log n) with probability 1 n k of declaring a false positive. We give a deterministic algorithm whose time is O(n|ΣP | log m) 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45061-0_72">doi:10.1007/3-540-45061-0_72</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kx6jrpya3jdalifhx2avotsn2q">fatcat:kx6jrpya3jdalifhx2avotsn2q</a> </span>
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