A fast algorithm for optimal length-limited Huffman codes

Larmore, Lawrence L.; Hirschberg, Daniel S.

doi:10.1145/79147.79150

Cited by 103 publications

(70 citation statements)

References 10 publications

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“…This problem has a linear-time solution given sorted inputs; this solution was found for D = 2 in [8] and is found for D > 2 here. Let i ∈ {1, .…”

Section: Preliminariesmentioning

confidence: 67%

“…The minimum size constraint on codeword length requires a relatively simple change of solution range to [8]. The nonbinary coding generalization is a bit more involved; it requires first modifying the Package-Merge algorithm to allow for an arbitrary numerical base (binary, ternary, etc.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [8], monotonicity allows trading off a constant factor of time for drastically reduced space complexity for lengthlimited binary codes. We extend this to the bounded-length problem.…”

Section: Theoremmentioning

confidence: 99%

“…In Section II, we present a brief review of the relevant literature before extending to D-ary codes a notation first presented in [6]. This notation aids in solving the problem in question by reformulating it as an instance of the Dary Coin Collector's problem, presented in the section as an extension of the original (binary) Coin Collector's problem [8]. An extension of the Package-Merge algorithm solves this problem; we introduce the reduction and resulting algorithm in Section III.…”

Section: Introductionmentioning

confidence: 99%

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D-ary Bounded-Length Huffman Coding

Baer

2007

2007 IEEE International Symposium on Information Theory

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Abstract-Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many practical applications, is one such variant, in which codes are restricted to the set of codes in which none of the n codewords is longer than a given length, lmax. Binary lengthlimited coding can be done in O(nlmax) time and O(n) space via the widely used Package-Merge algorithm. In this paper the Package-Merge approach is generalized without increasing complexity in order to introduce a minimum codeword length, lmin, to allow for objective functions other than the minimization of expected codeword length, and to be applicable to both binary and nonbinary codes; nonbinary codes were previously addressed using a slower dynamic programming approach. These extensions have various applications -including faster decompressionand can be used to solve the problem of finding an optimal code with limited fringe, that is, finding the best code among codes with a maximum difference between the longest and shortest codewords. The previously proposed method for solving this problem was nonpolynomial time, whereas solving this using the novel algorithm requires only O(n(lmax − lmin)2 ) time and O(n) space.

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“…This problem has a linear-time solution given sorted inputs; this solution was found for D = 2 in [8] and is found for D > 2 here. Let i ∈ {1, .…”

Section: Preliminariesmentioning

confidence: 67%

Section: Preliminariesmentioning

confidence: 99%

“…In [8], monotonicity allows trading off a constant factor of time for drastically reduced space complexity for lengthlimited binary codes. We extend this to the bounded-length problem.…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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D-ary Bounded-Length Huffman Coding

Baer

2007

2007 IEEE International Symposium on Information Theory

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“…This prediction is furnished by a requantized measurement for each pixel made during a baseline cadence interval, and this baseline measurement is updated every 48 cadences (which is a software parameter) starting with the first cadence collected after return to science mode. The residuals from the baseline value are entropically encoded using a length-limited Huffman code [24][25][26] that limits the code words to no more than 24 bits. Huffman codes compress data streams by representing common symbols with short binary code words and uncommon symbols with long code words .…”

Section: Length-limited Huffman Codingmentioning

confidence: 99%

Front Matter: Volume 8152

Hoover¹,

Davies²,

Levin³

et al. 2011

SPIE Proceedings

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Sponsored and Published by SPIEDownloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 30 Apr 2019 Terms of Use: https://www.spiedigitallibrary.org/terms-of-useThe papers included in this volume were part of the technical conference cited on the cover and title page. Papers were selected and subject to review by the editors and conference program committee. Some conference presentations may not be available for publication. The papers published in these proceedings reflect the work and thoughts of the authors and are published herein as submitted. The publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.Please use the following format to cite material from this book:Author ( Copying of material in this book for internal or personal use, or for the internal or personal use of specific clients, beyond the fair use provisions granted by the U.S. Copyright Law is authorized by SPIE subject to payment of copying fees. The Transactional Reporting Service base fee for this volume is $18.00 per article (or portion thereof), which should be paid directly to the Copyright Clearance Center (CCC), 222 Rosewood Drive, Danvers, MA 01923. Payment may also be made electronically through CCC Online at copyright.com. Other copying for republication, resale, advertising or promotion, or any form of systematic or multiple reproduction of any material in this book is prohibited except with permission in writing from the publisher. The CCC fee code is 0277-786X/11/$18.00.Printed in the United States of America.Publication of record for individual papers is online in the SPIE Digital Library. SPIEDigitalLibrary.orgPaper Numbering: Proceedings of SPIE follow an e-First publication model, with papers published first online and then in print and on CD-ROM. Papers are published as they are submitted and meet publication criteria. A unique, consistent, permanent citation identifier (CID) number is assigned to each article at the time of the first publication. Utilization of CIDs allows articles to be fully citable as soon as they are published online, and connects the same identifier to all online, print, and electronic versions of the publication. SPIE uses a six-digit CID article numbering system in which:The first four digits correspond to the SPIE volume number. The last two digits indicate publication order within the volume using a Base 36 numbering system employing both numerals and letters. These two-number sets start with 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B … 0Z, followed by 10-1Z, 20-2Z, etc. The CID number appears on each page of the manuscript. The complete citation is used on the first page, and an abbreviated version on subsequent pages. Numbers in the index correspond to the last two digits of the six-digit CID number. Since launch, Kepler has announced the discovery of 17 exoplanets, including a system of six transiting a Sun-like star, Kepler-11, and the first confirmed rocky planet, Kepler-10b, with a radius of 1.4 tha...

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Decoding prefix codes

Liddell

Moffat

2006

Softw: Pract. Exper.

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Minimum‐redundancy prefix codes have been a mainstay of research and commercial compression systems since their discovery by David Huffman more than 50 years ago. In this experimental evaluation we compare techniques for decoding minimum‐redundancy codes, and quantify the relative benefits of recently developed restricted codes that are designed to accelerate the decoding process. We find that table‐based decoding techniques offer fast operation, provided that the size of the table is kept relatively small, and that approximate coding techniques can offer higher decoding rates than Huffman codes with varying degrees of loss of compression effectiveness. Copyright © 2006 John Wiley & Sons, Ltd.

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A fast algorithm for optimal length-limited Huffman codes

Abstract: An O ( nL )-time algorithm is introduced for constructing an optimal Huffman code for a weighted alphabet of size n , where each code string must have length no greater than L . The algorithm uses O ( n ) space.

Cited by 103 publications

References 10 publications

D-ary Bounded-Length Huffman Coding

D-ary Bounded-Length Huffman Coding

Front Matter: Volume 8152

Decoding prefix codes

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