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="" 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="">doi:10.1007/3-540-45061-0_72</a> <a target="_blank" rel="external noopener" href="">fatcat:kx6jrpya3jdalifhx2avotsn2q</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> </button> </a>