Combinatorial Algorithms: Generation, Enumeration, and Search, 1st Edition (Hardback) book cover

Combinatorial Algorithms

Generation, Enumeration, and Search, 1st Edition

By Donald L. Kreher, Douglas R. Stinson

CRC Press

344 pages

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Hardback: 9780849339882
pub: 1998-12-18
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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.

  • 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

    Table of Contents

    Structures and Algorithms

    What are Combinatorial Algorithms?

    What are Combinatorial Structures?

    What are Combinatorial Problems?


    Analysis of Algorithms

    Complexity Classes

    Data Structures

    Algorithm Design Techniques

    Generating Elementary Combinatorial Objects

    Combinatorial Generation


    k-Element Subsets


    More Topics in Combinatorial Generation

    Integer Partitions

    Set Partitions, Bell and Stirling Numbers

    Labeled Trees

    Catalan Families

    Backtracking Algorithms


    A General Backtrack Algorithm

    Generating All Cliques

    Estimating the Size of a Backtrack Tree

    Exact Cover

    Bounding Functions


    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


    Permutation Groups

    Orbits of Subsets

    Coset Representatives

    Orbits of k-tuples

    Generating Objects Having Automorphisms

    Computing Isomorphism



    Computing Certificates

    Isomorphism of Other Structures

    Basis Reduction


    Theoretical Development

    A Reduced Basis Algorithm

    Solving Systems of Integer Equations

    The Merkle-Hellman Knapsack System


    Algorithm Index

    Problem Index


    About the Series

    Discrete Mathematics and Its Applications

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    COMPUTERS / Operating Systems / General
    MATHEMATICS / General
    MATHEMATICS / Number Theory
    MATHEMATICS / Combinatorics