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Longest Common Extensions with Recompression

Author Tomohiro I



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Tomohiro I

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Tomohiro I. Longest Common Extensions with Recompression. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 18:1-18:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CPM.2017.18

Abstract

Given two positions i and j in a string T of length N, a longest common extension (LCE) query asks for the length of the longest common prefix between suffixes beginning at i and j. A compressed LCE data structure stores T in a compressed form while supporting fast LCE queries. In this article we show that the recompression technique is a powerful tool for compressed LCE data structures. We present a new compressed LCE data structure of size O(z lg (N/z)) that supports LCE queries in O(lg N) time, where z is the size of Lempel-Ziv 77 factorization without self-reference of T. Given T as an uncompressed form, we show how to build our data structure in O(N) time and space. Given T as a grammar compressed form, i.e., a straight-line program of size n generating T, we show how to build our data structure in O(n lg (N/n)) time and O(n + z lg (N/z)) space. Our algorithms are deterministic and always return correct answers.
Keywords
  • Longest Common Extension (LCE) queries
  • compressed data structure
  • grammar compressed strings
  • Straight-Line Program (SLP)

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