The Rightmost Equal-Cost Position Problem

LZ77-based compression schemes compress the input text by replacing factors in the text with an encoded reference to a previous occurrence formed by the couple (length, offset). For a given factor, the smallest is the offset, the smallest is the resulting compression ratio. This is optimally achieved by using the rightmost occurrence of a factor in the previous text. Given a cost function, for instance the minimum number of bits used to represent an integer, we define the Rightmost Equal-Cost Position (REP) problem as the problem of finding one of the occurrences of a factor which cost is equal to the cost of the rightmost one. We present the Multi-Layer Suffix Tree data structure that, for a text of length n, at any time i, it provides REP(LPF) in constant time, where LPF is the longest previous factor, i.e. the greedy phrase, a reference to the list of REP({set of prefixes of LPF}) in constant time and REP(p) in time O(|p| log log n) for any given pattern p

Less redundant codes for variable size dictionaries

We report on a family of variable-length codes with less redundancy than the flat code used in most of the variable size dictionary-based compression methods. The length of codes belonging to this family is still bounded above by [log_2/ |D|] where |D| denotes the dictionary size. We describe three of these codes, namely, the balanced code, the phase-in-binary code (PB), and the depth-span code (DS). As the name implies, the balanced code is constructed by a height balanced tree, so it has the shortest average codeword length. The corresponding coding tree for the PB code has an interesting property that it is made of full binary phases, and thus the code can be computed efficiently using simple binary shifting operations. The DS coding tree is maintained in such a way that the coder always finds the longest extendable codeword and extends it until it reaches the maximum length. It is optimal with respect to the code-length contrast. The PB and balanced codes have almost similar improvements, around 3% to 7% which is very close to the relative redundancy in flat code. The DS code is particularly good in dealing with files with a large amount of redundancy, such as a running sequence of one symbol. We also did some empirical study on the codeword distribution in the LZW dictionary and proposed a scheme called dynamic block shifting (DBS) to further improve the codes' performance. Experiments suggest that the DBS is helpful in compressing random sequences. From an application point of view, PB code with DBS is recommended for general practical usage

Real-time and distributed applications for dictionary-based data compression

The greedy approach to dictionary-based static text compression can be executed by a finite state machine. When it is applied in parallel to different blocks of data independently, there is no lack of robustness even on standard large scale distributed systems with input files of arbitrary size. Beyond standard large scale, a negative effect on the compression effectiveness is caused by the very small size of the data blocks. A robust approach for extreme distributed systems is presented in this paper, where this problem is fixed by overlapping adjacent blocks and preprocessing the neighborhoods of the boundaries. Moreover, we introduce the notion of pseudo-prefix dictionary, which allows optimal compression by means of a real-time semi-greedy procedure and a slight improvement on the compression ratio obtained by the distributed implementations

Parallel image compression

A parallel compression algorithm for the 16,384 processor MPP machine was developed. The serial version of the algorithm can be viewed as a combination of on-line dynamic lossless test compression techniques (which employ simple learning strategies) and vector quantization. These concepts are described. How these concepts are combined to form a new strategy for performing dynamic on-line lossy compression is discussed. Finally, the implementation of this algorithm in a massively parallel fashion on the MPP is discussed

Optimal Parsing for Dictionary Text Compression

Dictionary-based compression algorithms include a parsing strategy to transform the input text into a sequence of dictionary phrases. Given a text, such process usually is not unique and, for compression purpose, it makes sense to find one of the possible parsing that minimize the final compression ratio. This is the parsing problem. An optimal parsing is a parsing strategy or a parsing algorithm that solve the parsing problem taking account of all the constraints of a compression algorithm or of a class of homogeneous compression algorithms. Compression algorithm constrains are, for instance, the dictionary itself, i.e. the dynamic set of available phrases, and how much a phrase weights on the compressed text, i.e. the number of bits of which the codeword representing such phrase is composed, also denoted as the encoding cost of a dictionary pointer. In more than 30th years of history of dictionary based text compression, while plenty of algorithms, variants and extensions appeared and while dictionary approach to text compression became one of the most appreciated and utilized in almost all the storage and communication processes, only few optimal parsing algorithms were presented. Many compression algorithms still leaks optimality of their parsing or, at least, proof of optimality. This happens because there is not a general model of the parsing problem that includes all the dictionary based algorithms and because the existing optimal parsing algorithms work under too restrictive hypothesis. This work focus on the parsing problem and presents both a general model for dictionary based text compression called Dictionary-Symbolwise Text Compression theory and a general parsing algorithm that is proved to be optimal under some realistic hypothesis. This algorithm is called iii Dictionary-Symbolwise Flexible Parsing and it covers almost all of the known cases of dictionary based text compression algorithms together with the large class of their variants where the text is decomposed in a sequence of symbols and dictionary phrases. In this work we further consider the case of a free mixture of a dictionary compressor and a symbolwise compressor. Our Dictionary-Symbolwise Flexible Parsing covers also this case. We have indeed an optimal parsing algorithm in the case of dictionary-symbolwise compression where the dictionary is prefix closed and the cost of encoding dictionary pointer is variable. The symbolwise compressor is any classical one that works in linear time, as many common variable-length encoders do. Our algorithm works under the assumption that a special graph that will be described in the following, is well defined. Even if this condition is not satisfied, it is possible to use the same method to obtain almost optimal parses. In detail, when the dictionary is LZ78-like, we show how to implement our algorithm in linear time. When the dictionary is LZ77-like our algorithm can be implemented in time O(n log n). Both have O(n) space complexity. Even if the main aim of this work is of theoretical nature, some experimental results will be introduced to underline some practical effects of the parsing optimality in terms of compression performance and to show how to improve the compression ratio by building extensions Dictionary- Symbolwise of known algorithms. Finally, some more detailed experiments are hosted in a devoted appendix