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Almost Optimal Searching of Maximal Subrepetitions in a Word

Author

Listed:
  • Roman Kolpakov

    (Faculty of Mechanics and Mathematics, Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991 Moscow, Russia
    Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Vavilov St. 40, 119333 Moscow, Russia)

Abstract

For some fixed δ such that 0 < δ < 1 , a δ -subrepetition in a word is a factor whose exponent is less than 2 but is not less than 1 + δ (the exponent of the factor is the ratio of the factor length to its minimal period). The δ -subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter while preserving its minimal period. In the paper, we propose an algorithm for searching all maximal δ -subrepetitions in a word of length n in O ( n δ log 1 δ ) time (the lower bound for this time is Ω ( n δ ) ). It improves the previous known time complexity bounds for solving this problem.

Suggested Citation

  • Roman Kolpakov, 2022. "Almost Optimal Searching of Maximal Subrepetitions in a Word," Mathematics, MDPI, vol. 10(19), pages 1-27, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3569-:d:929858
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