Tighter upper bounds on the exact complexity of string matching

Cole, Richard and Hariharan, Ramesh (1997) Tighter upper bounds on the exact complexity of string matching. In: SIAM Journal on Computing, 26 (3). pp. 803-856.

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Abstract

This paper considers how many character comparisons are needed to nd 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 of n + O(n=m) character comparisons, following preprocessing. Specifically, we 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 and requires O(m) space and O(m2) time for preprocessing. The current best lower bound for online algorithms is n + 16 7m+27 (n − m) character comparisons for m = 16k + 19, for any integer k>=1, and for general algorithms is n + 2 m+3 (n −m) character comparisons, for m = 2k + 1, for any integer k >=1.

Item Type:	Journal Article
Publication:	SIAM Journal on Computing
Publisher:	Society for Industrial and Applied Mathematics
Additional Information:	Copyright for this article belongs to Society for Industrial and Applied Mathematics (SIAM)
Keywords:	string matching;exact complexity;comparisons;periodicity
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	29 May 2004
Last Modified:	19 Sep 2010 04:12
URI:	http://eprints.iisc.ac.in/id/eprint/87

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