1st Edition

# Combinatorial Algorithms Generation, Enumeration, and Search

344 Pages
by CRC Press

342 Pages
by CRC Press

344 Pages
by CRC Press

Also available as eBook on:

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:

• Combinations
• Permutations
• Graphs
• Designs

• Many classical areas are covered as well as new research topics not included in most existing texts, such as:
• Group algorithms
• Graph isomorphism
• Hill-climbing
• 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.
• Structures and Algorithms
What are Combinatorial Algorithms?
What are Combinatorial Structures?
What are Combinatorial Problems?
O-Notation
Analysis of Algorithms
Complexity Classes
Data Structures
Algorithm Design Techniques
Generating Elementary Combinatorial Objects
Combinatorial Generation
Subsets
k-Element Subsets
Permutations
More Topics in Combinatorial Generation
Integer Partitions
Set Partitions, Bell and Stirling Numbers
Labeled Trees
Catalan Families
Backtracking Algorithms
Introduction
A General Backtrack Algorithm
Generating All Cliques
Estimating the Size of a Backtrack Tree
Exact Cover
Bounding Functions
Branch-and-Bound
Heuristic Search
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
Groups
Permutation Groups
Orbits of Subsets
Coset Representatives
Orbits of k-tuples
Generating Objects Having Automorphisms
Computing Isomorphism
Introduction
Invariants
Computing Certificates
Isomorphism of Other Structures
Basis Reduction
Introduction
Theoretical Development
A Reduced Basis Algorithm
Solving Systems of Integer Equations
The Merkle-Hellman Knapsack System
Bibliography
Algorithm Index
Problem Index
Index

### Biography

Kreher, Donald L.; Stinson, Douglas R.