Entropy, Search, Complexity

1. Front Matter

   Pages 1-8

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2. Two Colors and More

   • Martin Aigner

   Pages 9-26

3. Coding with Feedback and Searching with Lies

   • Christian Deppe

   Pages 27-70

4. Nonadaptive and Trivial Two-Stage Group Testing with Error-Correcting d ^e-Disjunct Inclusion Matrices

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

   Pages 71-83

5. Model Identification Using Search Linear Models and Search Designs

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

   Pages 85-112

6. Information Topologies with Applications

   • Peter Harremoës

   Pages 113-150

7. Reinforced Random Walk

   • Michael Keane

   Pages 151-158

8. Quantum Source Coding and Data Compression

   • Dénes Petz

   Pages 159-178

9. Information Theory at the Service of Science

   • Flemming Topsøe

   Pages 179-207

10. Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey)

    • Paul Vitányi

    Pages 209-232

11. Recognition Problems in Combinatorial Search

    • Gábor Wiener

    Pages 233-264

The present volume is a collection of survey papers in the ?elds given in the title. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. The volume is slightly related to the twin conferences “Search And Communication Complexity” and “Information Theory In Mathematics” held at Balatonlelle, Hungary in 2000. These conferences led us to believe that there is a need for such a collection of papers. The paper written by Martin Aigner starts with the following relatively new search problem. Given n boolean variables as input one has to ?nd one of them whose value is in majority. The goal is to minimize the number of tests needed for this where one test is to compare two input variables for equality. The paper surveys the large set of problems and results which grew out of this one. In the traditional search model an unknown element is sought in a ?nite set, based on the information that the unknown element is or is not in some (asked) subsets. A variant is when a 0,1 function is given on the underlying set, and only the values of this function at the unknown element x is sought rather than x itself. This is called the recognition problem.

• algorithm
• algorithms
• calculus
• coding
• combinatorics
• communication
• complexity
• computer science
• data compression
• entropy
• group
• information
• information theory
• mathematics
• topology
• algorithm analysis and problem complexity

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

  Imre Csiszár, Gyula O. H. Katona, Gábor Tardos

• Budapest University of Technology and Economics, Budapest, Hungary

  Gábor Wiener

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