Tighter Lower Bounds on the Exact Complexity of String Matching

The paper considers the exact number of character comparisons needed to nd all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + 9 4(m+1)) n character comparisons is obtained. For general algorithms, a lower bound of about (1 + 2 m+3) n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 + 8 3(m+1)) n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by nding patterns with interesting combinatorial properties. It is also shown that for some patterns oo-line algorithms can be more eecient than on-line algorithms.