TY - GEN

T1 - Function Matching: Algorithms, Applications and a Lower Bound

AU - Amihood, A.

AU - Aumann, Y.

AU - Cole, R.

AU - Lewenstein, M.

AU - Porat, E.

N1 - Place of conference:Eindhoven, The Netherlands

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://link.springer.com/chapter/10.1007/3-540-45061-0_72

M3 - Conference contribution

BT - 30th International Colloquium on Automata, Languages and Programming, (ICALP),

PB - Springer Berlin Heidelberg

ER -