- Author:
- Liviu Cornel Tinta
This thesis deals with repetitions in strings, tandem or independent. Tandem repetitions are encoded into maximal repetitions, called runs. We investigate the "runs" conjecture, which claims that the maximum number of runs in a string of length n is at most n . We almost solve the conjecture by proving the bound 1.029 n using a combination of theory and computer verification. This bound is by far the best one and is sufficient for all practical purposes.
For independent repetitions, we consider the longest common extension (LCE) problem that, given a string s and two positions i and j , asks for the longest common prefixes of the suffixes of s that start at i and j , respectively. We give very simple algorithms that use up to 24 times less space and are 5 times faster in practice.
An application of our fast LCE algorithm to approximate string search is presented. We give a modification of the algorithm of Landau and Vishkin that uses 5.6 times less space and runs up to 20 times faster in practice.
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