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Parallel data compression
Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested
Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation
Given a static reference string and a source string , a relative
compression of with respect to is an encoding of as a sequence of
references to substrings of . Relative compression schemes are a classic
model of compression and have recently proved very successful for compressing
highly-repetitive massive data sets such as genomes and web-data. We initiate
the study of relative compression in a dynamic setting where the compressed
source string is subject to edit operations. The goal is to maintain the
compressed representation compactly, while supporting edits and allowing
efficient random access to the (uncompressed) source string. We present new
data structures that achieve optimal time for updates and queries while using
space linear in the size of the optimal relative compression, for nearly all
combinations of parameters. We also present solutions for restricted and
extended sets of updates. To achieve these results, we revisit the dynamic
partial sums problem and the substring concatenation problem. We present new
optimal or near optimal bounds for these problems. Plugging in our new results
we also immediately obtain new bounds for the string indexing for patterns with
wildcards problem and the dynamic text and static pattern matching problem
Self-organizing lists on the Xnet
The first parallel designs for implementing self-organizing lists on the Xnet interconnection network are presented. Self-organizing lists permute the order of list entries after an entry is accessed according to some update hueristic. The heuristic attempts to place frequently requested entries closer to the front of the list. This paper outlines Xnet systems for self-organizing lists under the move-to-front and transpose update heuristics. Our novel designs can be used to achieve high-speed lossless text compression
Arithmetic coding revisited
Over the last decade, arithmetic coding has emerged as an important compression tool. It is now the method of choice for adaptive coding on multisymbol alphabets because of its speed,
low storage requirements, and effectiveness of compression. This article describes a new implementation of arithmetic coding that incorporates several improvements over a widely used earlier version by Witten, Neal, and Cleary, which has become a de facto standard. These improvements include fewer multiplicative operations, greatly extended range of alphabet sizes and symbol probabilities, and the use of low-precision arithmetic, permitting implementation by fast shift/add operations. We also describe a modular structure that separates the coding, modeling, and probability estimation components of a compression system. To motivate the improved coder, we consider the needs of a word-based text compression program. We report a range of experimental results using this and other models. Complete source code is available
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
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts
We study the approximate string matching and regular expression matching
problem for the case when the text to be searched is compressed with the
Ziv-Lempel adaptive dictionary compression schemes. We present a time-space
trade-off that leads to algorithms improving the previously known complexities
for both problems. In particular, we significantly improve the space bounds,
which in practical applications are likely to be a bottleneck
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