Reduction Ratio of the IS-Algorithm: Worst and Random Cases

Author Vincent Jugé

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Author Details

Vincent Jugé
  • LIGM, CNRS, Univ Gustave Eiffel, F77454 Marne-la-Vallée, France

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Vincent Jugé. Reduction Ratio of the IS-Algorithm: Worst and Random Cases. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word w into another word, called the reduced word of w, that will be at least twice shorter; then, the algorithm recursively computes the suffix array of the reduced word. In this article, we study the reduction ratio of the IS-algorithm, i.e., the ratio between the lengths of the input word and the word obtained after reducing k times the input word. We investigate both worst cases, in which we find precise results, and random cases, where we prove some strong convergence phenomena. Finally, we prove that, if the input word is a randomly chosen word of length n, we should not expect much more than log(log(n)) recursive function calls.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Word combinatorics
  • Suffix array
  • IS algorithm


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