Combinatorial Algorithms: Generation, Enumeration, and Search

by Donald L. Kreher, Douglas R. Stinson

Overview

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.

Product Details

ISBN-13:	9781000141375
Publisher:	CRC Press
Publication date:	09/23/2020
Series:	Discrete Mathematics and Its Applications
Sold by:	Barnes & Noble
Format:	eBook
Pages:	344
File size:	33 MB
Note:	This product may take a few minutes to download.

About the Author

Kreher, Donald L.; Stinson, Douglas R.

Table of Contents

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

Editorial Reviews

"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

From the Publisher