Combinatorial Algorithms: Generation, Enumeration, and Search

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.
  • 1134793547
    Combinatorial Algorithms: Generation, Enumeration, and Search

    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.
  • 86.99 In Stock
    Combinatorial Algorithms: Generation, Enumeration, and Search

    Combinatorial Algorithms: Generation, Enumeration, and Search

    Combinatorial Algorithms: Generation, Enumeration, and Search

    Combinatorial Algorithms: Generation, Enumeration, and Search

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    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

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