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

Amihood Amir, Yonatan Aumann, Richard Cole, Moshe Lewenstein, Ely Porat
2003 Lecture Notes in Computer Science  
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 » ... 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.
doi:10.1007/3-540-45061-0_72 fatcat:kx6jrpya3jdalifhx2avotsn2q