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Tighter bounds on the exact complexity of string matching

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2 Author(s)
Cole, Richard ; Courant Inst., New York Univ., NY, USA ; Hariharan, R.

The paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form n + O(n/m) character comparisons, following preprocessing. Specifically, the authors show an upper bound of n+8/3(m+1)(n-m) character comparisons. This bound is achieved by an online algorithm which performs O(n) work in total, requires O(m) space and O(m2) time for preprocessing. In addition the following lower bounds are shown: for online algorithms, a bound of n+11/5(m+1) (n-m) character comparisons for m = 10 + 11 k, for any integer k ⩾ 1, and for general algorithms, a bound of n+2(n-m)/m+3 character comparisons, for m=2 k+l, for any integer k⩾1

Published in:

Foundations of Computer Science, 1992. Proceedings., 33rd Annual Symposium on

Date of Conference:

24-27 Oct 1992