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Fast Entropy-Bounded String Dictionary Look-Up with Mismatches

Authors Pawel Gawrychowski, Gad M. Landau, Tatiana Starikovskaya

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Author Details

Pawel Gawrychowski
  • University of Wrocław, Wrocław, 50-137, Poland
Gad M. Landau
  • University of Haifa, Haifa, 3498838, Israel
Tatiana Starikovskaya
  • DIENS, École normale supérieure, PSL Research University, Paris, 75005, France

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Pawel Gawrychowski, Gad M. Landau, and Tatiana Starikovskaya. Fast Entropy-Bounded String Dictionary Look-Up with Mismatches. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.66

Abstract

We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(w d log^{1+epsilon} d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + log^k d + occ) query time and uses O(w d log^k d) extra bits of space.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Dictionary look-up
  • Hamming distance
  • compact data structures

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