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The WARMUP Algorithm: A Lagrangean Construction of Length Restricted Huffman Codes
 Departamento de Inform'atica, PUCRJ, Rio de
, 1996
"... : Given an alphabet fa 1 ; : : : ; ang with corresponding set of weights fw 1 ; : : : ; wng, and a number L dlog ne, we introduce an O(n log n+n log w) algorithm for constructing a suboptimal prefix code with restricted maximal length L, where w is the highest presented weight. The number of additi ..."
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: Given an alphabet fa 1 ; : : : ; ang with corresponding set of weights fw 1 ; : : : ; wng, and a number L dlog ne, we introduce an O(n log n+n log w) algorithm for constructing a suboptimal prefix code with restricted maximal length L, where w is the highest presented weight. The number of additional bits per symbol generated by our code is not greater than 1=/ L\Gammadlog(n+dlog ne\GammaL)e\Gamma2 when L ? dlog ne + 1, where / is the golden ratio 1:618. An important feature of the proposed algorithm is its implementation simplicity. The algorithm is basically a selected sequence of Huffman trees construction for modified weights. Keywords: Prefix codes, Huffman Trees, Lagragean Duality Resumo: Dado um alfabeto fa 1 ; : : : ; ang com pesos correspondentes fw 1 ; : : : ; wng e um n'umero L dlog ne, n'os apresentamoso um algoritmo de de complexidade O(n log n + n log w)para construit c'odigos de prefixo sub'otimos com restric~ao de comprimento L, onde w 'e o maior peso do dado co...
Robust Universal Complete Codes for Transmission and Compression
 Discrete Applied Mathematics
, 1996
"... Several measures are defined and investigated, which allow the comparison of codes as to their robustness against errors. Then new universal and complete sequences of variablelength codewords are proposed, based on representing the integers in a binary Fibonacci numeration system. Each sequence is ..."
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Several measures are defined and investigated, which allow the comparison of codes as to their robustness against errors. Then new universal and complete sequences of variablelength codewords are proposed, based on representing the integers in a binary Fibonacci numeration system. Each sequence is constant and need not be generated for every probability distribution. These codes can be used as alternatives to Huffman codes when the optimal compression of the latter is not required, and simplicity, faster processing and robustness are preferred. The codes are compared on several "reallife" examples. 1. Motivation and Introduction Let A = fA 1 ; A 2 ; \Delta \Delta \Delta ; An g be a finite set of elements, called cleartext elements, to be encoded by a static uniquely decipherable (UD) code. For notational ease, we use the term `code' as abbreviation for `set of codewords'; the corresponding encoding and decoding algorithms are always either given or clear from the context. A code i...
Skeleton Trees for the Efficient Decoding of Huffman Encoded Texts
 Information Retrieval
, 1997
"... : A new data structure is investigated, which allows fast decoding of texts encoded by canonical Huffman codes. The storage requirements are much lower than for conventional Huffman trees, O(log 2 n) for trees of depth O(log n), and decoding is faster, because a part of the bitcomparisons nec ..."
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: A new data structure is investigated, which allows fast decoding of texts encoded by canonical Huffman codes. The storage requirements are much lower than for conventional Huffman trees, O(log 2 n) for trees of depth O(log n), and decoding is faster, because a part of the bitcomparisons necessary for the decoding may be saved. Empirical results on large reallife distributions show a reduction of up to 50% and more in the number of bit operations. The basic idea is then generalized, yielding further savings. This is an extended version of a paper which has been presented at the 8th Annual Symposium on Combinatorial Pattern Matching (CPM'97), and appeared in its proceedings, pp. 6575.  1  1.
Accelerating Boyer Moore Searches on Binary Texts Shmuel
"... The Boyer and Moore (BM) pattern matching algorithm is considered as one of the best, but its performance is reduced on binary data. Yet, searching in binary texts has important applications, such as compressed matching. The paper shows how, by means of some precomputed tables, one may implement th ..."
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The Boyer and Moore (BM) pattern matching algorithm is considered as one of the best, but its performance is reduced on binary data. Yet, searching in binary texts has important applications, such as compressed matching. The paper shows how, by means of some precomputed tables, one may implement the BM algorithm also for the binary case without referring to bits, and processing only entire blocks such as bytes or words, thereby significantly reducing the number of comparisons. Empirical comparisons show that the new variant performs better than regular binary BM and even than BDM. Key words: PACS:
Practical Use of The Warmup Algorithm on LengthRestricted Coding
 the Proceedings of the Fourth Latin American Workshop on String Processing
, 1997
"... . In this paper we present an efficient implementation of the WARMUP Algorithm for the construction of lengthrestricted prefix codes. This algorithm has O(n log n + n log wn) worst case time complexity, where n is the number of symbols of the source alphabet and wn is the largest weight of the ..."
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. In this paper we present an efficient implementation of the WARMUP Algorithm for the construction of lengthrestricted prefix codes. This algorithm has O(n log n + n log wn) worst case time complexity, where n is the number of symbols of the source alphabet and wn is the largest weight of the alphabet. An important feature of the proposed algorithm is its implementation simplicity. The algorithm is basically a selected sequence of Huffman trees construction for modified weights. The proposed implementation has the same time complexity, but requires only additional O(1) space. We also report some empirical experiments showing that this algorithm provides good compression and speed performances. 1 Introduction An important problem in the field of Coding and Information Theory is the Binary Prefix Code Problem. Given an alphabet \Sigma = fa 1 ; : : : ; ang and a corresponding set of positive weights fw 1 ; : : : ; wng, the problem is to find a prefix code for \Sigma that mi...