Time Complexity of Knuth-Morris-Pratt String Matching Algorithm

This project centers on the evaluation for the time complexity of Knuth-Morris-Pratt(KMP) string matching algorithm. String matching problem is to locate a pattern string within a larger string. The best performance in terms of asymptotic time complexity is currently linear, given by the KMP algorithm. In this algorithm, firstly a prefix for the pattern string is computed and then based on this prefix, only linear time is needed to find the pattern string in the larger string. In details of both steps, the prefix computation and matcher, two loops are needed, where one goes over the whole string and the other loop travels back to some point of the prefix array. I test these two steps with a large number of random input strings, of which the lengths are different, and for evaluation, ranges of the strings are also under control to simulate the various cases. As much as possible, I expect to get the tight analysis of the KMP algorithm’s time complexity. During these tests, the numbers of basic operations are recorded and then linear analysis is conducted, giving the coefficients of linear regression and the correlation coefficient. Finally, together with the analysis, it is concluded that the linear time complexity is validated based on the experiments.