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A simpler analysis of BurrowsWheeler based compression
 In Proc. of the 17th Symposium on Combinatorial Pattern Matching (CPM ’06). SpringerVerlag LNCS
, 2006
"... In this paper we present a new technique for worstcase analysis of compression algorithms which are based on the BurrowsWheeler Transform. We deal mainly with the algorithm proposed by Burrows and Wheeler in their first paper on the subject [6], called bw0. This algorithm consists of the following ..."
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In this paper we present a new technique for worstcase analysis of compression algorithms which are based on the BurrowsWheeler Transform. We deal mainly with the algorithm proposed by Burrows and Wheeler in their first paper on the subject [6], called bw0. This algorithm consists of the following three essential steps: 1) Obtain the BurrowsWheeler Transform of the text, 2) Convert the transform into a sequence of integers using the movetofront algorithm, 3) Encode the integers using Arithmetic code or any order0 encoding (possibly with runlength encoding). We achieve a strong upper bound on the worstcase compression ratio of this algorithm. This bound is significantly better than bounds known to date and is obtained via simple analytical techniques. Specifically, we show that for any input string s, and µ> 1, the length of the compressed string is bounded by µ · sHk(s)+ log(ζ(µ)) · s  + µgk + O(log n) where Hk is the kth order empirical entropy, gk is a constant depending only on k and on the size of the alphabet, and ζ(µ) = 1 1 1 µ+ 2 µ+... is the standard zeta function. As part of the analysis we prove a result on the compressibility of integer sequences, which is of independent interest. Finally, we apply our techniques to prove a worstcase bound on the compression ratio of a compression algorithm based on the BurrowsWheeler Transform followed by distance coding, for which worstcase guarantees have never been given. We prove that the length of the compressed string is bounded by 1.7286 · sHk(s) + gk + O(log n). This bound is better than the bound we give for bw0.
EFFICIENT ALGORITHMS FOR ZECKENDORF ARITHMETIC
"... We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for ..."
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We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for multiplication, division and squareroot extraction are also discussed.
On the Usefulness of Fibonacci Compression Codes
, 2004
"... Recent publications advocate the use of various variable length codes for which each codeword consists of an integral number of bytes in compression applications using large alphabets. This paper shows that another tradeoff with similar properties can be obtained by Fibonacci codes. These are fixed ..."
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Cited by 2 (1 self)
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Recent publications advocate the use of various variable length codes for which each codeword consists of an integral number of bytes in compression applications using large alphabets. This paper shows that another tradeoff with similar properties can be obtained by Fibonacci codes. These are fixed codeword sets, using binary representations of integers based on Fibonacci numbers of order m ≥ 2. Fibonacci codes have been used before, and this paper extends previous work presenting several novel features. In particular, the compression efficiency is analyzed and compared to that of dense codes, and various tabledriven decoding routines are suggested.
Working with Compressed Concordances
"... Abstract. A combination of new compression methods is suggested in order to compress the concordance of a large Information Retrieval system. The methods are aimed at allowing most of the processing directly on the compressed file, requesting decompression, if at all, only for small parts of the acc ..."
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Abstract. A combination of new compression methods is suggested in order to compress the concordance of a large Information Retrieval system. The methods are aimed at allowing most of the processing directly on the compressed file, requesting decompression, if at all, only for small parts of the accessed data, saving I/O operations and CPU time.
The BurrowsWheeler compression algorithm is even better than what you have thought
, 2005
"... The best compression algorithm today for English text is based on the BurrowsWheeler transform. This algorithm (whose common implementation is bzip2) consists of the following three essential steps: 1) Obtain the BurrowsWheeler transform of the text, 2) Convert the transform into a sequence of int ..."
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The best compression algorithm today for English text is based on the BurrowsWheeler transform. This algorithm (whose common implementation is bzip2) consists of the following three essential steps: 1) Obtain the BurrowsWheeler transform of the text, 2) Convert the transform into a sequence of integers using the movetofront algorithm, 3) Encode the integers using arithmetic code or any order0 encoding (possibly with run length encoding). In this paper we achieve a strong bound on the worstcase compression ratio of this algorithm, that is significantly better than bounds known to date and is obtained via simple analytical techniques. Specifically, for any input string s, and µ> 1, the length of the compressed string is bounded by µ · sHk(s) + log(ζ(µ)) · s  + gk where Hk is the kth order empirical entropy, gk is a constant depending only on k and on the size of the alphabet, and ζ(µ) = 1 1 µ + 1 2 µ +... is the standard zeta function. In fact we prove a stronger result: That this bound without the additive term gk holds when we replace Hk(s) by the sum of the logarithms of the integers obtain by the movetofront encoding of the transform. This refined bound is tight and close to the actual compression achieved in practice. To obtain this result we prove a tight result on the compressibility of integer sequences, which is of independent interest. 1
Editorial Preface
"... Today, it is incredible to consider that in 1969 men landed on the moon using a computer with a 32kilobyte memory that was only programmable by the use of punch cards. In 1973, Astronaut Alan Shepherd participated in the first computer "hack " while orbiting the moon in his landing vehicl ..."
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Today, it is incredible to consider that in 1969 men landed on the moon using a computer with a 32kilobyte memory that was only programmable by the use of punch cards. In 1973, Astronaut Alan Shepherd participated in the first computer "hack " while orbiting the moon in his landing vehicle, as two programmers back on Earth attempted to "hack" into the duplicate computer, to find a way for Shepherd to convince his computer that a catastrophe requiring a mission abort was not happening; the successful hack took 45 minutes to accomplish, and Shepherd went on to hit his golf ball on the moon. Today, the average computer sitting on the desk of a suburban home office has more computing power than the entire U.S. space program that put humans on another world!! Computer science has affected the human condition in many radical ways. Throughout its history, its developers have striven to make calculation and computation easier, as well as to offer new means by which the other sciences can be advanced. Modern massivelyparalleled supercomputers help scientists with previously unfeasible problems such as fluid dynamics, complex function convergence, finite element analysis and realtime weather dynamics. At IJACSA we believe in spreading the subject knowledge with effectiveness in all classes of audience. Nevertheless, the promise of increased engagement requires that we consider how this might be accomplished, delivering uptodate and authoritative coverage of advanced computer science and applications. Throughout our archives, new ideas and technologies have been welcomed, carefully critiqued, and discarded or