Computation over APT Compressed Data

Avivit Levy, Dana Shapira

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The Arithmetic Progressions Tree (APT) is an encoding of a monotonic sequence ℒ in [1..n]. Previous work on APT coding focused on its theoretical and experimental compression guarantees. This paper is the first to consider computations over APT compressed data. In particular: (1) We show how to perform a search for any sub-sequence of the monotone sequence ℒ in time proportional to the query sub-sequence length multiplied by the size of the APT compressed representation of ℒ. (2) We show how, given the APT compressed representation of the monotone sequence ℒ, we can find a minimum run-length of ℒ in constant time, a maximum run-length of ℒ in O(log n) time, and all runs of ℒ in constant time plus the output size. (3) Most importantly, we show how, given the APT compressed representation of the monotone sequence ℒ, we can answer whether a periodic pattern P appears in ℒ in O(log n) time and report its locations in the output size time. (4) In addition, we improve the APT construction algorithm time and space complexity.

Original languageEnglish
Title of host publicationProceedings - DCC 2024
Subtitle of host publication2024 Data Compression Conference
EditorsAli Bilgin, James E. Fowler, Joan Serra-Sagrista, Yan Ye, James A. Storer
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages10
ISBN (Electronic)9798350385878
StatePublished - 2024
Externally publishedYes
Event2024 Data Compression Conference, DCC 2024 - Snowbird, United States
Duration: 19 Mar 202422 Mar 2024

Publication series

NameData Compression Conference Proceedings
ISSN (Print)1068-0314


Conference2024 Data Compression Conference, DCC 2024
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© 2024 IEEE.


  • APT compression
  • Arithmetic progressions
  • Compact Data Structures
  • Monotonic sequences
  • Periodic patterns


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