@inproceedings{78443ceb967340ca8012482475b94985,
title = "Computation over APT Compressed Data",
abstract = "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.",
keywords = "APT compression, Arithmetic progressions, Compact Data Structures, Monotonic sequences, Periodic patterns",
author = "Avivit Levy and Dana Shapira",
note = "Publisher Copyright: {\textcopyright} 2024 IEEE.; 2024 Data Compression Conference, DCC 2024 ; Conference date: 19-03-2024 Through 22-03-2024",
year = "2024",
doi = "10.1109/DCC58796.2024.00023",
language = "الإنجليزيّة",
series = "Data Compression Conference Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "153--162",
editor = "Ali Bilgin and Fowler, \{James E.\} and Joan Serra-Sagrista and Yan Ye and Storer, \{James A.\}",
booktitle = "Proceedings - DCC 2024",
address = "الولايات المتّحدة",
}