Computational Discrete Mathematics: Advanced Lectures (Lecture Notes in Computer Science, 2122)

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. Lattice Paths and Determinants....Pages 1-12 The Nearest Neighbor....Pages 13-24 Explicit and Implicit Enforcing - Randomized Optimization....Pages 25-46 Codes over Z 4 ....Pages 47-55 Degree Bounds for Long Paths and Cycles in k -Connected Graphs....Pages 56-60 Data Structures for Boolean Functions BDDs — Foundations and Applications....Pages 61-78 Scheduling under Uncertainty: Bounding the Makespan Distribution....Pages 79-97 Random Graphs, Random Triangle-Free Graphs, and Random Partial Orders....Pages 98-118 Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches....Pages 119-135 Check Character Systems and Anti-symmetric Mappings....Pages 136-147 Algorithms in Pure Mathematics....Pages 148-158 Coloring Hamming Graphs, Optimal Binary Codes, and the 0/1-Borsuk Problem in Low Dimensions....Pages 159-171

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.

The 12 selected lectures presented in this volume provide 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. The essence of mathematics is proving theorems - and so, that is what mathematicians do: they prove theorems.