Graphs, dynamic programming, and finite games / by A. Kaufmann ; translated by Henry C. Sneyd.

Format:

Book

Author/Creator:

Kaufmann, A. (Arnold), 1911-

Series:

Mathematics in science and engineering ; v. 36.

Mathematics in science and engineering ; v. 36

Standardized Title:

Méthodes et modèles de la recherche opérationnelle. Volume 2. English

Language:

English

Subjects (All):

Games of strategy (Mathematics).

Graph theory.

Programming (Mathematics).

Physical Description:

1 online resource (503 p.)

Place of Publication:

New York : Academic Press, 1967.

Language Note:

English

Summary:

Graphs, Dynamic Programming and Finite Games

Contents:

Front Cover; Graphs, Dynamic Programming, and Finite Games; Copyright Page; Contents; Foreword; Foreword to the French Edition; Preface to the French Edition; Part 1. Methods and Models; Chapter I. Graphs; 1. Introduction; 2. The Use of Points and Arcs to Represent Structures; 3. Principal Concepts Used in the Theory of Graphs; 4. Scheduling and Sequencing Problems; 5. Tree of a Graph; 6. Search for an Optimal Flow in a Network. The Ford-Fulkerson Algorithm; 7. Application of the Theory of Graphs to Psychosociology; 8. Automatic Textual Emendation. Search for Lost Manuscripts

Chapter II. Dynamic Programming9. Introduction; 10. Bellman's Theorem of Optimality; 11. First Example of Multistage Optimization; 12. Distribution of Investments; 13. A Purchasing Problem; 14. Decisions in the Face of Uncertainty; 15. Two Examples of Dynamic Programming in the Face of an Uncertain Future; 16. Theorem of Optimality in the Case of Uncertainty. Discrete Systems; 17. Interval of Anticipation. Dynamic Programming with Adaptation; 18. Effect of Introducing a Rate of Interest; Chapter III. The Theory of Games of Strategy; 19. Introduction; 20. Game on a Rectangular Matrix

21. Point of Equilibrium of a Rectangular Game22. Pure Strategy and Mixed Strategy; 23. Various Properties; 24. Use in Concrete Cases of Competition; 25. Use in Cases of a ""Struggle against Nature""; 26. Choice of a Criterion; 27. The Theory of Statistical Decision; 28. Multistage Games with Two Players; Part II. Mathematical Developments; Symbols for the Theory of Sets Used in Part II; Chapter IV. The Principal Properties of Graphs; 29. Introduction; 30. Definition and Figure; 31. Oriented Concepts; 32. Nonoriented Concepts; 33. Product and Sum of Graphs; 34. Various Generalizations

35. Typical Numbers in a p-Graph36. Separation or Shortest Path in a Graph; 37. Transport Network; 38. Linking Two Disjoint Sets; 39. Hamiltonian Path and Circuit; 40. Center and Radius of a Graph; 41. Network (Strongly Connected Graph without a Loop); 42. Matrix Associated with a Graph; 43. Incidence Matrix; 44. Tree. Arborescence; 45. Eulerian Chain and Cycle; 46. Point and Set of Articulation. Connectivity Number; 47. Planar Graphs; 48. Mapping a Graph into a Graph; Chapter V. Mathematical Properties of Dynamic Programming; 49. Introduction; 50. Formulas for Multistage Optimization

51. Convergence of a Dynamic Program in a Limited Future52. Difficulty of the Final Calculations; 53. Uncertain Development Using a Markovian Chain; 54. The z-Transform; 55. Using the z-Transform to Study Markovian Chains; 56. Markovian Chain with Transition Values; 57. Study of Some Important Special Cases; 58. Dynamic Programming in a Case of Uncertainty; 59. Dynamic Program with Markovian Chain; 60. Long Term Situation (Case of a Fully Ergodic Matrix); 61. Iterative Optimization; 62. Long Term Strategy When the Chain Is Not Fully Ergodic; 63. Discounted Value of the Revenue

64. Applying Dynamic Programming to a Real Problem

Notes:

Translation of v. 2 of Methodes et modeles de la recherche operationnelle.

Includes bibliographical references and index.

ISBN:

1-282-28949-7

9786612289491

0-08-095543-6

OCLC:

316568670