Computational Discrete Mathematics

1. Front Matter

   Pages I-VII

   PDF

2. Lattice Paths and Determinants

   • Martin Aigner

   Pages 1-12

3. The Nearest Neighbor

   • Helmut Alt

   Pages 13-24

4. Explicit and Implicit Enforcing - Randomized Optimization

   • Bernd Gärtner, Emo Welzl

   Pages 25-46

5. Codes over Z ₄

   • Tor Helleseth

   Pages 47-55

6. Degree Bounds for Long Paths and Cycles in k-Connected Graphs

   • Heinz Adolf Jung

   Pages 56-60

7. Data Structures for Boolean Functions BDDs — Foundations and Applications

   • Christoph Meinel, Christian Stangier

   Pages 61-78

8. Scheduling under Uncertainty: Bounding the Makespan Distribution

   • Rolf H. Möhring

   Pages 79-97

9. Random Graphs, Random Triangle-Free Graphs, and Random Partial Orders

   • Hans Jürgen Prömel, Anusch Taraz

   Pages 98-118

10. Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches

    • Günter Rote

    Pages 119-135

11. Check Character Systems and Anti-symmetric Mappings

    • Ralph-Hardo Schulz

    Pages 136-147

12. Algorithms in Pure Mathematics

    • Gernot Stroth

    Pages 148-158

13. Coloring Hamming Graphs, Optimal Binary Codes, and the 0/1-Borsuk Problem in Low Dimensions

    • Günter M. Ziegler

    Pages 159-171

14. Back Matter

    Pages 172-172

    PDF

This book is based on a graduate education program on computational discrete mathematics run for several years in Berlin, Germany, as a joint effort of theoretical computer scientists and mathematicians in order to support doctoral students and advanced ongoing education in the field of discrete mathematics and algorithmics.
The 12 selected lectures by leading researchers presented in this book provide recent research results and advanced topics in a coherent and consolidated way. Among the areas covered are combinatorics, graph theory, coding theory, discrete and computational geometry, optimization, and algorithmic aspects of algebra.

• Computer
• Discrete mathematics
• Mapping
• algorithms
• coding
• coding theory
• combinatorics
• computational algebra
• computational algorithms
• computational geometry
• computational mathematics
• data structures
• geometry
• graph computations
• randomization
• algorithm analysis and problem complexity

• Institut für Informatik, Freie Universität Berlin, Berlin, Germany

  Helmut Alt

Policies and ethics