Efficient Comparison Based String Matching

AbstractWe study the exact number of symbol comparisons that are required to solve the string matching problem and present a family of efficient algorithms. Unlike previous string matching algorithms, the algorithms in this family do not "forget" results of comparisons, what makes their analysis much simpler. In particular, we give a linear-time algorithm that finds all occurrences of a pattern of length m in a text of length n in [formula] comparisons. The pattern preprocessing takes linear time and makes at most 2m comparisons. This algorithm establishes that, in general, searching for a long pattern is easier than searching for a short one. We also show that any algorithm in the family of the algorithms presented must make at least [formula] symbol comparisons, for m = 2k − 1 and any integer k ≥ 1