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Entropy, Search, Complexity

Part of the Bolyai Society Mathematical Studies Book Series (volume 16)

Editors: Csiszár, Imre; Katona, Gyula O. H.; Tardos, Gábor; Wiener, Gábor

DOI: 10.1007/978-3-540-32777-6

ISBN: 978-3-540-32573-4

Publisher: Springer Berlin Heidelberg - Springer Journals

Jan 1, 2007

1 - 10 of 10 Chapters

LitStream

Chapter 1Two Colors and More

Aigner, Martin

Pages: 9 –26

[Suppose we are given n balls colored with two colors. How many color-comparisons are needed to produce a ball of the majority color? The answer (first given by Saks and Werman) is M(n) = n−B(n), where B(n) is the number of 1’s in the binary representation of n. We consider in this paper several...
LitStream

Chapter 2Coding with Feedback and Searching with Lies

Deppe, Christian

Pages: 27 –70

[This paper gives a broad overview of the area of searching with errors and the related field of error-correcting coding. In the vast literature regarding this problem, many papers simultaneously deal with various sorts of restrictions on the searching protocol. We partition this survey into...
LitStream

Chapter 3Nonadaptive and Trivial Two-Stage Group Testing with Error-Correcting de-Disjunct Inclusion Matrices

D’Yachkov, Arkadii G.; Macula, Anthony J.; Vilenkin, Pavel A.

Pages: 71 –83

[We discuss three types of inclusion matrices (subset, subspace and sequence). We exhibit their disjunct properties and their applications to error-correcting nonadaptive group testing. Under some limited conditions, these structures are optimal for their disjunct properties.]
LitStream

Chapter 4Model Identification Using Search Linear Models and Search Designs

Ghosh, S.; Shirakura, T.; Srivastava, J. N.

Pages: 85 –112

[In designing an experiment, we often assume a model and then find a best design satisfying one or more optimal properties under the assumed model. This approach works well when we are absolutely sure about the assumed model that it will fit the experimental data adequately. In reality, we are...
LitStream

Chapter 5Information Topologies with Applications

Harremoës, Peter

Pages: 113 –150

[Topologies related to information divergence are introduced. The conditional limit theorem is taken as motivating example, and simplified proofs of the relevant theorems are given. Continuity properties of entropy and information divergence are discussed.]
LitStream

Chapter 6Reinforced Random Walk

Keane, Michael

Pages: 151 –158

[One of the distinguishing properties of the present scientific method is reproducibility. In one of its guises, probability theory is based on statistical reproduction, near certainty being obtained of truth of statements by averaging over long term to remove randomness occurring in individual...
LitStream

Chapter 7Quantum Source Coding and Data Compression

Petz, Dénes

Pages: 159 –178

[This lecture is intended to be an easily accessible first introduction to quantum information theory. The field is large and it is not completely covered even by the recent monograph [15]. Therefore the simple topic of data compression is selected to present some ideas of the theory. Classical...
LitStream

Chapter 8Information Theory at the Service of Science

Topsøe, Flemming

Pages: 179 –207

[Information theory is becoming more and more important for many fields. This is true for engineering- and technology-based areas but also for more theoretically oriented sciences such as probability and statistics.]
LitStream

Chapter 9Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey)

Vitányi, Paul

Pages: 209 –232

[Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort,...
LitStream

Chapter 10Recognition Problems in Combinatorial Search

Wiener, Gábor

Pages: 233 –264

[We survey some recent results concerning recognition problems. Recognition problems are special combinatorial search problems, where we need not find the hidden element x itself, just compute the value f(x) for a given function f. We mainly use the approaches of classical search theory and...

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