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The Smallest Grammar Problem
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... This paper addresses the smallest grammar problem: What is the smallest contextfree grammar that generates exactly one given string σ? This is a natural question about a fundamental object connected to many fields, including data compression, Kolmogorov complexity, pattern identification, and addi ..."
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This paper addresses the smallest grammar problem: What is the smallest contextfree grammar that generates exactly one given string σ? This is a natural question about a fundamental object connected to many fields, including data compression, Kolmogorov complexity, pattern identification, and addition chains. Due to the problem’s inherent complexity, our objective is to find an approximation algorithm which finds a small grammar for the input string. We focus attention on the approximation ratio of the algorithm (and implicitly, worstcase behavior) to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature. Our first results are a variety of hardness results, most notably that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569 unless P = NP. 8568 We then bound approximation ratios for several of the bestknown grammarbased compression algorithms, including LZ78, BISECTION, SEQUENTIAL, LONGEST MATCH, GREEDY, and REPAIR. Among these, the best upper bound we show is O(n 1/2). We finish by presenting two novel algorithms with exponentially better ratios of O(log 3 n) and O(log(n/m ∗)), where m ∗ is the size of the smallest grammar for that input. The latter highlights a connection between grammarbased compression and LZ77.
Crowd Modelling in Collaborative Virtual Environments
 ACM VRST
, 1998
"... This paper presents a crowd modelling method in Collaborative Virtual Environment (CVE) which aims to create a sense of group presence to provide a more realistic virtual world. An adaptive display is also presented as a key element to optimise the needed information to keep an acceptable frame rate ..."
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Cited by 40 (15 self)
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This paper presents a crowd modelling method in Collaborative Virtual Environment (CVE) which aims to create a sense of group presence to provide a more realistic virtual world. An adaptive display is also presented as a key element to optimise the needed information to keep an acceptable frame rate during crowd visualisation. This system has been integrated in the several CVE platforms which will be presented at the end of this paper. 1.1 Keywords Autonomous agents, virtual crowds, virtual environments.
Multineuronal firing patterns in the signal from eye to brain. Neuron 2003;37:499–511
"... to address, because three important components must all come together. First, one must record from many neurons simultane ..."
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Cited by 35 (0 self)
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to address, because three important components must all come together. First, one must record from many neurons simultane
Efficient decoding of prefix codes
 COMMUNICATIONS OF THE ACM
, 1990
"... We discuss representations of prefix codes and the corresponding storage space and decoding time requirements. We assume that a dictionary of words to be encoded has been defined and that a prefix code appropriate to the dictionary has been constructed. The encoding operation becomes simple given th ..."
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Cited by 33 (0 self)
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We discuss representations of prefix codes and the corresponding storage space and decoding time requirements. We assume that a dictionary of words to be encoded has been defined and that a prefix code appropriate to the dictionary has been constructed. The encoding operation becomes simple given these assumptions and given an appropriate parsing strategy, therefore we concentrate on decoding. The application which led us to this work constrains the use of internal memory during the decode operation. As a result, we seek a method of decoding which has a small memory requirement.
Lossless Compression of Volume Data
, 1994
"... Data in volume form consumes an extraordinary amount of storage space. For efficient storage and transmission of such data, compression algorithms are imperative. However, most volumetric datasets are used in biomedicine and other scientific applications where lossy compression is unacceptable. We p ..."
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Cited by 32 (1 self)
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Data in volume form consumes an extraordinary amount of storage space. For efficient storage and transmission of such data, compression algorithms are imperative. However, most volumetric datasets are used in biomedicine and other scientific applications where lossy compression is unacceptable. We present a lossless datacompression algorithm which, being oriented specifically for volume data, achieves greater compression performance than generic compression algorithms that are typically available on modern computer systems. Our algorithm is a combination of differential pulsecode modulation (DPCM) and Huffman coding and results in compression of around 50% for a set of volume data files. I. Introduction Compression for efficient storage and transmission of digital data has become routine as the application of such data has grown. Several common datacompression programs are readily available on many computers to fight the burgeoning demand for storage space. These programs are typica...
DNABased Cryptography
 5th DIMACS Workshop on DNA Based Computers, MIT
, 1999
"... Recent research has considered DNA as a medium for ultrascale computation and for ultracompact information storage. One potential key application is DNAbased, molecular cryptography systems. We present some procedures for DNAbased cryptography based on onetimepads that are in principle unbre ..."
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Cited by 30 (5 self)
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Recent research has considered DNA as a medium for ultrascale computation and for ultracompact information storage. One potential key application is DNAbased, molecular cryptography systems. We present some procedures for DNAbased cryptography based on onetimepads that are in principle unbreakable. Practical applications of cryptographic systems based on onetime pads are limited in conventional electronic media by the size of the onetimepad; however DNA provides a much more compact storage medium, and an extremely small amount of DNA su#ces even for huge onetimepads. We detail procedures for two DNA onetimepad encryption schemes: (i) a substitution method using libraries of distinct pads, each of which defines a specific, randomly generated, pairwise mapping; and (ii) an XOR scheme utilizing molecular computation and indexed, random key strings. These methods can be applied either for the encryption of natural DNA or for artificial DNA encoding binary data. In the latter case, we also present a novel use of chipbased DNA microarray technology for 2D data input and output.
Structures of String Matching and Data Compression
, 1999
"... This doctoral dissertation presents a range of results concerning efficient algorithms and data structures for string processing, including several schemes contributing to sequential data compression. It comprises both theoretic results and practical implementations. We study the suffix tree data st ..."
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Cited by 29 (0 self)
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This doctoral dissertation presents a range of results concerning efficient algorithms and data structures for string processing, including several schemes contributing to sequential data compression. It comprises both theoretic results and practical implementations. We study the suffix tree data structure, presenting an efficient representation and several generalizations. This includes augmenting the suffix tree to fully support sliding window indexing (including a practical implementation) in linear time. Furthermore, we consider a variant that indexes naturally wordpartitioned data, and present a lineartime construction algorithm for a tree that represents only suffixes starting at word boundaries, requiring space linear in the number of words. By applying our sliding window indexing techniques, we achieve an efficient implementation for dictionarybased compression based on the LZ77 algorithm. Furthermore, considering predictive source
Compression of Correlated BitVectors
 Information Systems
, 1990
"... : Bitmaps are data structures occurring often in information retrieval. They are useful; they are also large and expensive to store. For this reason, considerable effort has been devoted to finding techniques for compressing them. These techniques are most effective for sparse bitmaps. We propose a ..."
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Cited by 28 (2 self)
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: Bitmaps are data structures occurring often in information retrieval. They are useful; they are also large and expensive to store. For this reason, considerable effort has been devoted to finding techniques for compressing them. These techniques are most effective for sparse bitmaps. We propose a preprocessing stage, in which bitmaps are first clustered and the clusters used to transform their member bitmaps into sparser ones, that can be more effectively compressed. The clustering method efficiently generates a graph structure on the bitmaps. In some situations, it is desired to impose restrictions on the graph; finding the optimal graph satisfying these restrictions is shown to be NPcomplete. The results of applying our algorithm to the Bible is presented: for some sets of bitmaps, our method almost doubled the compression savings. 1. Introduction Textual Information Retrieval Systems (IRS) are voracious consumers of computer storage resources. Most conspicuous, of course, is the...
'Computing' as information compression by multiple alignment, unification and search
 Journal of Universal Computer Science
, 1999
"... This paper argues that the operations of a `Universal Turing Machine' (UTM) and equivalent mechanisms such as the `Post Canonical System' (PCS)  which are widely accepted as definitions of the concept of `computing'  may be interpreted as information compression by multiple alig ..."
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Cited by 28 (14 self)
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This paper argues that the operations of a `Universal Turing Machine' (UTM) and equivalent mechanisms such as the `Post Canonical System' (PCS)  which are widely accepted as definitions of the concept of `computing'  may be interpreted as information compression by multiple alignment, unification and search (ICMAUS). The motivation for this interpretation is that it suggests ways in which the UTM/PCS model may be augmented in a proposed new computing system designed to exploit the ICMAUS principles as fully as possible. The provision of a relatively sophisticated search mechanism in the proposed `SP' system appears to open the door to the integration and simplification of a range of functions including unsupervised inductive learning, bestmatch pattern recognition and information retrieval, probabilistic reasoning, planning and problem solving, and others. Detailed consideration of how the ICMAUS principles may be applied to these functions is outside the scope of this article but relevant sources are cited in this article.