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Minimal Suffix and Rotation of a Substring in Optimal Time

Author Tomasz Kociumaka

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Tomasz Kociumaka

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Tomasz Kociumaka. Minimal Suffix and Rotation of a Substring in Optimal Time. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 28:1-28:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CPM.2016.28

Abstract

For a text of length $n$ given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering such queries optimally: in constant time after linear-time preprocessing. This improves upon the results of Babenko et al. (CPM 2014), whose trade-off solution is characterized by Theta(n log n) product of these time complexities. Next, we extend our queries to support concatenations of O(1) substrings, for which the construction and query time is preserved. We apply these generalized queries to compute lexicographically minimal and maximal rotations of a given substring in constant time after linear-time preprocessing.

Our data structures mainly rely on properties of Lyndon words and Lyndon factorizations. We combine them with further algorithmic and combinatorial tools, such as fusion trees and the notion of order isomorphism of strings.

Subject Classification

Keywords
  • minimal suffix
  • minimal rotation
  • Lyndon factorization
  • substring canon- ization
  • substring queries

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