Generalizations of Length Limited Huffman Coding for Hierarchical Memory Settings

Banchhor, S and Gajjala, R and Sabharwal, Y and Sen, S (2021) Generalizations of Length Limited Huffman Coding for Hierarchical Memory Settings. In: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 15-17 Dec 2021, Virtual, Online.

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Abstract

In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study a special case of this problem that is closely related to the length limited Huffman coding (LLHC) problem; we call this the soft-length limited Huffman coding problem. In this version, there is a penalty associated with each of the n characters of the alphabet whose encodings exceed a specified bound D(� n) where the penalty increases linearly with the length of the encoding beyond D. The goal of the problem is to find a prefix-free encoding having minimum average code length and total penalty within a pre-specified bound P. This generalizes the LLHC problem. We present an algorithm to solve this problem that runs in time O(nD). We study a further generalization in which the penalty function and the objective function can both be arbitrary monotonically non-decreasing functions of the codeword length. We provide dynamic programming based exact and PTAS algorithms for this setting. © Shashwat Banchhor, Rishikesh Gajjala, Yogish Sabharwal, and Sandeep Sen.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Keywords:	Cost functions; Decoding; Dynamic programming; Encoding (symbols); Signal encoding, Average code length; Coding problems; Cost models; Cost-function; Encoding schemes; Generalisation; Hierarchical memory; Huffman coding; Prefix-free codes; Prefix-free encoding, Approximation algorithms
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	27 Jan 2022 11:47
Last Modified:	27 Jan 2022 11:47
URI:	http://eprints.iisc.ac.in/id/eprint/71039

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