Analyzes algorithms in generation, enumeration, search, and optimization as well as basic algorithmic paradigmsExamines topics not found in other texts, including group algorithms, graph isomorphism, hill-climbing, and heuristic search algorithmsProvides accessible reading of modern combinatorial techniquesUnifies diverse scientific and mathematical research into one volumeIncludes pseudocode description of all algorithms
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:
Many classical areas are covered as well as new research topics not included in most existing texts, such as:
Heuristic search algorithms
This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
Table of Contents
Structures and Algorithms
What are Combinatorial Algorithms?
What are Combinatorial Structures?
What are Combinatorial Problems?
Analysis of Algorithms
Algorithm Design Techniques
Generating Elementary Combinatorial Objects
More Topics in Combinatorial Generation
Set Partitions, Bell and Stirling Numbers
A General Backtrack Algorithm
Generating All Cliques
Estimating the Size of a Backtrack Tree
Introduction to Heuristic Algorithms
Design Strategies for Heuristic Algorithms
A Steepest-Ascent Algorithm for Uniform Graph Partition
A Hill-Climbing Algorithm for Steiner Triple Systems
Two Heuristic Algorithms for the Knapsack Problem
A Genetic Algorithm for the Traveling Salesman Problem
Groups and Symmetry
Orbits of Subsets
Orbits of k-tuples
Generating Objects Having Automorphisms
Isomorphism of Other Structures
A Reduced Basis Algorithm
Solving Systems of Integer Equations
The Merkle-Hellman Knapsack System
"Very clear exposition. I jumped right into [the] heuristic methods chapter and understood it almost instantly..."
- Dean H. Judson, Ph.D., Nevada State Demographer
"…book serves as an introduction to the basic problems and methods…style is clear, transparent…The algorithmic problems are always considered and they are in the center of the discussion…has a fresh approach to combinatorics that is available for readers, students in computer science, electrical engineering without any background in mathematics."
- Péter Hajnal, Acta Science Math