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Hierarchical Relative Lempel-Ziv Compression

Authors Philip Bille , Inge Li Gørtz , Simon J. Puglisi , Simon R. Tarnow

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Author Details

Philip Bille
  • Department of Computer Science and Applied Mathematics, Technical University of Denmark, Lyngby, Denmark
Inge Li Gørtz
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark
Simon J. Puglisi
  • Helsinki Institute for Information Technology (HIIT), Finland
  • Department of Computer Science, University of Helsinki, Finland
Simon R. Tarnow
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark

Funding

This work was supported in part by the Academy of Finland via grants 339070 and 351150 and the Danish Research Council via grant DFF-8021-002498.

Cite AsGet BibTex

Philip Bille, Inge Li Gørtz, Simon J. Puglisi, and Simon R. Tarnow. Hierarchical Relative Lempel-Ziv Compression. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SEA.2023.18

Abstract

Relative Lempel-Ziv (RLZ) parsing is a dictionary compression method in which a string S is compressed relative to a second string R (called the reference) by parsing S into a sequence of substrings that occur in R. RLZ is particularly effective at compressing sets of strings that have a high degree of similarity to the reference string, such as a set of genomes of individuals from the same species. With the now cheap cost of DNA sequencing, such datasets have become extremely abundant and are rapidly growing. In this paper, instead of using a single reference string for the entire collection, we investigate the use of different reference strings for subsets of the collection, with the aim of improving compression. In particular, we propose a new compression scheme hierarchical relative Lempel-Ziv (HRLZ) which form a rooted tree (or hierarchy) on the strings and then compress each string using RLZ with parent as reference, storing only the root of the tree in plain text. To decompress, we traverse the tree in BFS order starting at the root, decompressing children with respect to their parent. We show that this approach leads to a twofold improvement in compression on bacterial genome datasets, with negligible effect on decompression time compared to the standard single reference approach. We show that an effective hierarchy for a given set of strings can be constructed by computing the optimal arborescence of a completed weighted digraph of the strings, with weights as the number of phrases in the RLZ parsing of the source and destination vertices. We further show that instead of computing the complete graph, a sparse graph derived using locality-sensitive hashing can significantly reduce the cost of computing a good hierarchy, without adversely effecting compression performance.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Relative compression
  • Lempel-Ziv compression
  • RLZ
  • LZ77
  • string collections
  • compressed representation
  • data structures
  • efficient algorithms

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