Graphs, Algorithms and Optimization

Graphs, Algorithms and Optimization

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Description

Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms. Written in an accessible and informal style, this work covers nearly all areas of graph theory.
Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.
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Product details

  • Hardback | 504 pages
  • 162 x 236 x 32mm | 861.84g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 247 black & white illustrations, 247 black & white tables
  • 1584883960
  • 9781584883968
  • 1,320,385

Review quote

"The book is written in an easygoing style, and the proofs are concisely presented and easy to follow. [This book] would serve as a fine textbook for an undergraduate graph theory course for math majors. [I]t is well-written, the proofs are easy to follow, the figures complement the text, and the exercises are helpful to student understanding" - MAA Online "A valuable resource for mathematics and computer science students and professionalscontains a wealth of information on algorithms and the data structures needed to program them efficientlythe graph theory presented is rigorous, but the style is informal." - L'Enseignement Mathimatique
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Table of contents

GRAPHS AND THEIR COMPLEMENTS Degree sequences Analysis PATHS AND WALKS Complexity Walks The shortest path problem Weighted graphs and Dijkstra's algorithm Data structures. Floyd's algorithm SOME SPECIAL CLASSES OF GRAPHS Bipartite graphs Line graphs Moore graphs Euler tours TREES AND CYCLES Fundamental Co-trees and bonds Spanning tree algorithms THE STRUCTURE OF TREES Non-rooted Read's tree encoding algorithm Generating rooted trees Generating non-rooted trees Prufer sequences Spanning trees The matrix-tree theorem CONNECTIVITY Blocks Finding the blocks of a graph The depth-first search ALTERNATING PATHS AND MATCHINGS. The Hungarian algorithm Perfect matchings and 1-factorizations The subgraph problem Coverings in bipartite graphs Tutte's theorem NETWORK FLOWS Introduction The Ford-Fulkerson algorithm Matchings and flows Menger's theorems Disjoint paths and separating sets Notes HAMILTON CYCLES The crossover algorithm The Hamilton closure The extended multi-path algorithm The traveling salesman problem The ?TSP Christofides' algorithm DIGRAPHS Activity graphs, Critical paths Topological order Strong components An application to fabrics Tournaments Satisfiability GRAPH COLORINGS Cliques Mycielski's construction Critical graphs Chromatic polynomials Edge colorings NP-completeness PLANAR GRAPHS Jordan curves Graph minors Subdivisions Euler's formula Rotation systems Dual graphs Platonic solids Triangulations The sphere 5 Whitney's theorem Medial digraphs The 4-color problem Straight line drawings Kuratowski's theorem The Hopcroft-Tarjan Algorithm GRAPHS AND SURFACES Surfaces Graph embeddings Graphs on the torus Graphs on the projective plane LINEAR PROGRAMMING The simplex algorithm Cycling THE PRIMAL-DUAL ALGORITHM Alternate form of the primal and its dual Geometric interpretation Complementary slackness The dual of the shortest path problem The primal-dual algorithm DISCRETE LINEAR PROGRAMMING Backtracking Branch and bound Unimodular matrices BIBLIOGRAPHY INDEX
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