Function Matching: Algorithms, Applications and a Lower Bound

A. Amihood; Y. Aumann; R. Cole; M. Lewenstein; E. Porat

Function Matching: Algorithms, Applications and a Lower Bound

A. Amihood, Y. Aumann, R. Cole, M. Lewenstein, E. Porat

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	American English
Title of host publication	30th International Colloquium on Automata, Languages and Programming, (ICALP),
Publisher	Springer Berlin Heidelberg
State	Published - 2003

Bibliographical note

Place of conference:Eindhoven, The Netherlands

Cite this

@inproceedings{f130bb33922b4040bbbeb83011970203,

title = "Function Matching: Algorithms, Applications and a Lower Bound",

abstract = "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.",

author = "A. Amihood and Y. Aumann and R. Cole and M. Lewenstein and E. Porat",

note = "Place of conference:Eindhoven, The Netherlands",

year = "2003",

language = "American English",

booktitle = "30th International Colloquium on Automata, Languages and Programming, (ICALP),",

publisher = "Springer Berlin Heidelberg",

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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 -

Function Matching: Algorithms, Applications and a Lower Bound

Abstract

Bibliographical note

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