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Combinatorial Algorithms: Generation, Enumeration, and Search: Discrete Mathematics and Its Applications

Autor Donald L. Kreher, Douglas R. Stinson
en Limba Engleză Paperback – noi 2019
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.
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    Specificații

    ISBN-13: 9780367400156
    ISBN-10: 0367400154
    Pagini: 344
    Dimensiuni: 156 x 234 x 22 mm
    Greutate: 0.54 kg
    Ediția:1
    Editura: CRC Press
    Colecția CRC Press
    Seria Discrete Mathematics and Its Applications


    Public țintă

    Undergraduate

    Cuprins

    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

    Notă biografică

    Kreher, Donald L.; Stinson, Douglas R.

    Recenzii

    "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

    Descriere

    Combinatorial Algorithms: Generation, Enumeration, and Search thoroughly outlines and analyzes combinatorial algorithms for generation, enumeration, and search applications.