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 = PP ... 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)f(P) ... 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 language||American English|
|Title of host publication||International Colloquium on Automata, Languages, and Programming|
|Editors||Jos C. M. Baeten, Jan Karel Lenstra, Joachim Parrow, Gerhard J. Woeginger, Jan Karel, Lenstra Joachim, Parrow Gerhard, J. Woeginger|
|Publisher||Springer Berlin Heidelberg|
|State||Published - 2003|