SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Hypercube Problems - NTIN097
Title in English: Problémy na hyperkrychlích
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://ktiml.mff.cuni.cz/~gregor/hypercube/hypercube-course.htm
Guarantor: Mgr. Petr Gregor, Ph.D.
Class: Informatika Mgr. - Teoretická informatika
Classification: Informatics > Theoretical Computer Science
Annotation -
Last update: RNDr. Jan Hric (26.04.2019)
Many questions in various areas of theoretical computer science may be formulated as problems in hypercubes. The lecture offers an overview of selected problems studied in hypercubes with emphasis on applications in theoretical computer science. It assumes only elementary knowledge and it is suitable for students in the M.Sc. programme.
Aim of the course -
Last update: T_KTI (28.04.2015)

The course gives an introduction into the area of hypercube problems.

Course completion requirements -
Last update: Mgr. Petr Gregor, Ph.D. (07.06.2019)

Course is completed by exam. Requirements for exam and its form are described below.

Literature -
Last update: T_KTI (28.04.2015)
  • B. Bollobás, Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability, Cambridge University Press, Cambridge, 1986.
  • R. Hammack, W. Imrich, S. Klavžar, Handbook of Product Graphs, Second Edition, CRC Press, 2011.
  • S. Jukna, Extremal Combinatorics with Applications in Computer Science, Springer, Berlin, 2001.
  • F. T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann, San Mateo, 1992.
  • selected journal papers.

Requirements to the exam -
Last update: Mgr. Petr Gregor, Ph.D. (09.10.2017)

The exam consists of solving three sets of exercises during the semester and writing a research text on selected topic, e.g. a lecture scribe. Average exercise grade will cover 70% of the final mark, and the other 30% will be given for the graded text.

Syllabus -
Last update: T_KTI (28.04.2015)
  • Hypercube characterizations, basic properties.
  • Orbit and stabilizer theorem, group of automorphisms.
  • Parcial cubes, median graphs, convex expansion.
  • Nonexpansive maps, correspondence to 2-SAT.
  • Matchings, Gray codes, Hamiltonian decomposition.
  • Independent spanning trees, robustness of communication.
  • Shadows, intersecting systems, isoperimetric problems.
  • Linear layout problems, width parameters.
  • Influence of variables of boolean functions, harmonic analysis.
  • Packing and covering, applications of self-correcting codes.
  • Turán numbers and other extremal problems.

 
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