Combinatorial Algorithms Generation, Enumeration, and Search Discrete Mathematics and Its Applications Series
Auteurs : Kreher Donald L., Stinson Douglas R.
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:
Many classical areas are covered as well as new research topics not included in most existing texts, such as:
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.
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
Date de parution : 11-2019
15.6x23.4 cm
Thèmes de Combinatorial Algorithms :
Mots-clés :
Steiner Triple System; Hamiltonian Circuit; Isomorphism; Maximum Clique; Heuristic search algorithm; Backtracking Algorithm; Combinatorial algorithms; Traveling Salesman Problem; Backtracking algorithms; Maximum Clique Problem; Latin Square; Feasible Solution; Incidence Matrix; Vertex Set; Subset Sum Problem; Tabu Search Algorithm; Stirling Numbers; Automorphism Group; Gray Code; Neighborhood Search Strategy; Equitable Partition; Simulated Annealing Algorithm; Neighborhood Search; Bounding Function; Maximum Independent Set; Recombination Operation; Discrete Partition; Shortest Vector; Adjacency Matrix