Which patterns are hard to find? [String matching]

The paper considers the exact number of character comparisons needed to find 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 bound complement an on-line upper bound of about (1+⁸/_3(m+1)).n comparisons obtained recently by Cole and Hariharan (1992). The lower bounds are obtained by finding patterns with interesting combinatorial properties (these are the hard to find patterns). It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms