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Doubly-Periodic String Comparison

Authors Nikita Gaevoy, Boris Zolotov, Alexander Tiskin

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Theory of computation → Pattern matching
Keywords
  • String Comparison
  • periodic Strings
  • Longest common Subsequence
  • affine Hecke Monoid
  • affine sticky Braids

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Abstract

The longest common subsequence (LCS) problem is a fundamental algorithmic problem. Given a pair of strings, the problem asks for the length of the longest string that is a subsequence in both input strings. Among the many relatives of this problem, there is its natural version where one or both of input strings have periodic structure. The case where only one of the input strings is periodic has been considered before; in this work, we develop an efficient algorithm for the more difficult case where both input strings are periodic. The algorithm is based on the existing algebraic framework for the LCS problem, developed by the third author; in particular, we extend this framework to dealing with affine (i.e. doubly-infinite periodic) permutations instead of finite ones. Given input strings that are a k-repeat of a period of length m and an 𝓁-repeat of a period of length n, the resulting algorithm runs in time O(mn+n log n log k), which is a substantial improvement over existing approaches. The algorithm has been implemented by the first author; by running his code, one can process pairs of periodic input strings with lengths far beyond the reach of all known alternative algorithms.

Cite As Get BibTex

Nikita Gaevoy, Boris Zolotov, and Alexander Tiskin. Doubly-Periodic String Comparison. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.13

Author Details

Nikita Gaevoy
  • Department of Mathematics and Computer Science, St. Petersburg State University, Russia
  • The Faculty of Data and Decision Sciences, Technion, Haifa, Israel
Boris Zolotov
  • Department of Mathematics and Computer Science, St. Petersburg State University, Russia
Alexander Tiskin
  • Department of Mathematics and Computer Science, St. Petersburg State University, Russia

Funding

  • Zolotov, Boris: Research is supported by „Native towns“, a social investment program of PJSC „Gazprom Neft“.

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