Self-Alignments in Words and Their Applications

Abstracl This paper deals with the probabilistic analysis of some quantitative measures associated with periodicities in words, notably, the various values attained by the lengths of the longest common prefix of pairs of suffixes of a given word. Such values, that are called here self-alignments, playa crucial role in sever3J. algorithmic constructions, such as building the suffix tree or inverted file of a word, detecting squares and other repetitions in a word. computing substring statistics, etc. The probabilistic analysis of self-alignments is then used to study the expected time complexities of straightforward algorithmic solutions to these problems, and to compare such performances with those attained by more complex constructions.