NDLI: Practical Entropy-Bounded Schemes for O(1)-Range Minimum Queries

Content Provider	IEEE Xplore Digital Library
Author	Fischer, J. Heun, V. Stiihler, H.M.
Copyright Year	2008
Description	Author affiliation: Univ. Munchen, Munich (Fischer, J.; Heun, V.; Stiihler, H.M.)
Abstract	The Range Minimum Query (RMQ) Problem is to preprocess an array A of length n in 0(n) time such that subsequent on-line queries asking for the position of a minimal element between two specified indices can be obtained in constant time. Several solutions to this problem have been proposed, starting with Berkman and Vishkin's linear-space solution [6], and leading to a succinct solution using only 2n + o(n) bits in addition to the input array [12]. The theoretical contribution of this article is to push this latter approach one step further and show that for compressible input arrays the RMQ-information can be compressed as well. In particular, we show that information for 0(l)-RMQs can be stored within the same entropy bounds that are achieved by the currently best schemes for storing A itself in compressed form, while still being able to access O(logn) contiguous bits in O(l) time [10]. Two such entropy- bounded schemes for 0(l)-RMQs are developed, each with its own practical advantage. We test these two methods extensively and compare them to three other schemes for RMQs: the currently best non-succinct solution [2], and two succinct approaches: Sadakane's 4n + o(n)-bit solution [22], and our own 2n + o(n)-bit solution. The results of this practical evaluation are (1) the practical space consumptions of the non-compressed schemes scale surprisingly well with their theoretical guarantees, and (2) for compressible input arrays our new compressed schemes can indeed reduce the space, with little or no slowdown in query time.
Starting Page	272
Ending Page	281
File Size	301446
Page Count	10
File Format	PDF
ISBN	9780769531212
ISSN	10680314
DOI	10.1109/DCC.2008.45
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-03-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Data compression Entropy Data structures Testing Information retrieval Data flow computing Flow graphs Tree graphs Navigation Compressors entropy-bounded scheme range minimum query succinct data structure
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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