TY - GEN

T1 - Computation over APT Compressed Data

AU - Levy, Avivit

AU - Shapira, Dana

N1 - Publisher Copyright:
© 2024 IEEE.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - APT compression

KW - Arithmetic progressions

KW - Compact Data Structures

KW - Monotonic sequences

KW - Periodic patterns

UR - http://www.scopus.com/inward/record.url?scp=85194830368&partnerID=8YFLogxK

U2 - 10.1109/DCC58796.2024.00023

DO - 10.1109/DCC58796.2024.00023

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AN - SCOPUS:85194830368

T3 - Data Compression Conference Proceedings

SP - 153

EP - 162

BT - Proceedings - DCC 2024

A2 - Bilgin, Ali

A2 - Fowler, James E.

A2 - Serra-Sagrista, Joan

A2 - Ye, Yan

A2 - Storer, James A.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2024 Data Compression Conference, DCC 2024

Y2 - 19 March 2024 through 22 March 2024

ER -