Combinatorial Algorithms
Generation, Enumeration, and Search
1st Edition
Published on 23. September 2020
344 pages
978-1-000-10287-1 (ISBN)
Description
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.
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.
Reviews / Votes
"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."
- Peter Hajnal, Acta Science Math
More details
Series
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
ISBN-13
978-1-000-10287-1 (9781000102871)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
11/2019
1st Edition
CRC Press
€101.50
Shipment within 15-20 days
Book
12/1998
1st Edition
CRC Press
€198.20
Shipment within 15-20 days
Persons
Kreher, Donald L.; Stinson, Douglas R.
Content
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
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
