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- W1989204408 abstract "Given a pattern string of length n and an object string of length m, the string matching problem asks for the positions of all occurrences of the pattern in the object string. This paper investigates a generalization of string matching, in which the pattern is a sequence of pattern elements, each compatible with a set of symbols. The alphabet of symbols is infinite, with its members encoded in a finite alphabet. In contrast to standard string matching, which can be solved in simultaneous linear time and constant space, it is shown that generalized string matching requires a time-space product of $Omega ({{n^2 } / {log n}})$ on a powerful model of computation, when the alphabet is restricted to n symbols. Our proof uses a method of Borodin. The obvious algorithm for generalized string matching requires time $O(NM)$, where N is the length of the encoding of the pattern, and M is that of the object string. We describe an algorithm which solves generalized string matching in time $O(N + M + mN^{{1 / 2}} {operatorname{polylog}} (n))$." @default.
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- W1989204408 date "1987-12-01" @default.
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- W1989204408 title "Generalized String Matching" @default.
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- W1989204408 doi "https://doi.org/10.1137/0216067" @default.
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