عنوان

Boolean Methods in Operations Research and Related Areas

(Number (ISBN

3642858252

(Number (ISBN

9783642858253

Number

b544305

Title Proper

Boolean Methods in Operations Research and Related Areas

General Material Designation

[Book]

First Statement of Responsibility

P.L. Hammer ; S. Rudeanu

Edition Statement

Softcover reprint of the original 1st ed. 1968

Name of Publisher, Distributor, etc.

Berlin Springer Berlin

Date of Publication, Distribution, etc.

2014

Specific Material Designation and Extent of Item

XV, 331 Seiten in 1 Teil 235 x 155 mm

Series Title

Ökonometrie und Unternehmensforschung / Econometrics and Operations Research, 7

Text of Note

I.- I. Boolean Algebra.- 1. The Two-Element Boolean Algebra.- 2. Boolean Functions.- 3. Boolean Matrices and Determinants.- 4. The General Concept of Boolean Algebra.- 5. Boolean Algebras and Boolean Rings.- 6. Pseudo-Boolean Functions.- II. Boolean Equations.- A. Equations in an Arbitrary Boolean Algebra.- 1. The Single-Equation Form of a System of Boolean Equations and/or Inequalities.- 2. The Boolean Equation m one Unknown (Consistency and Solutions).- 3. Boolean Equations m n Unknowns: The Method of Successive Eliminations (Consistency and Solutions).- 4. The Lowenheim Form of the General Solution.- B. Equations in the Two-Element Boolean Algeha.- 5. The Method of Bifurcations.- 6. Families of Solutions.- C. Addendum.- 7. Other Researches Concerning Boolean Equations and their Generalizations.- III. Linear Pseudo-Boolean Equations and Inequalities.- 1. Linear Pseudo-Boolean Equations.- 2. Linear Pseudo-Boolean Inequalities.- 3. Systems of Pseudo-Boolean Equations and/or Inequalities.- 4. The Methods of R. Fortet and P. Camion.- IV. Nonlinear Pseudo-Boolean Equations and Inequalities.- 1. The Characteristic Function m the Linear Case.- 2. The Characteristic Function of a Nonlinear Equation or Inequality.- 3. The Characteristic Function for Systems.- 4. The Characteristic Function of Logical Conditions.- 5. Irredundant Solutions of the Characteristic Equation.- 6. The Pseudo-Boolean Form of the Characteristic Equation.- 7. The Methods of R. Fortet and P. Camion.- V. Minimization of Linear Pseudo-Boolean Functions.- 1. Using Partially Minimizing Points.- 2. Accelerated Linear Pseudo-Boolean Programming.- 3. The Method of P. Camion.- VI. Minimization of Nonlinear Pseudo-Boolean Functions.- A. Minima without Constraints.- 1. The Basic Algorithm.- B. Minima with Constraints.- 2. Lagrangean Multipliers.- 3. Minimization Using Families of Solutions.- 4. Minimization Using Parametric Forms of the Solutions.- 5. Extension of the Basic Algorithm.- VII. Extensions of Pseudo-Boolean Programming.- 1. Local Minima of Pseudo-Boolean Functions.- 2. Applications to the Theory of Graphs.- 3. Near-Minima of Pseudo-Boolean Functions.- 4. Minimax Problems m Pseudo-Boolean Programming.- 5. Fractional Pseudo-Boolean Programming.- II.- VIII. Integer Mathematical Programming.- 1. All-Integer Mathematical Programming.- 2. Mixed Integer-Continuous Mathematical Programming.- 3. Linear and Quadratic Continuous Programming.- 4. Discrete-Variable Problems.- IX. Connectedness and Path Problems in Graphs.- 1. Basic Concepts m Graph Theory: Paths, Circuits, Connectedness.- 2 Unitary Incidence-Matrices.- 3. Incidence Matrices.- 4. The Algebraic Closure of Graphs.- 5. Decompositions of Graphs.- 6. Latin Multiplication.- 7. Hamiltoman Paths and Circuits.- 8. Using Free Boolean Algebras.- 9. Boolean Proofs of Graph-Theoretical Properties.- X. Stable Sets, Kernels, and Chromatic Decompositions of Graphs.- 1. Definitions and Interpretations.- 2 Internally Stable Sets.- 3. Externally Stable Sets.- 4. Kernels of Graphs.- 5. Chromatic Decompositions.- 6. The Four Colouring Problem.- XI. Matchings of Bipartite Graphs.- 1. Bipartite Graphs.- 2. Assignment and Transportation Problems.- 3. Systems of Representatives.- XII. Flows in Networks and Chains in Partially Ordered Sets.- 1. Flows m Networks.- 2. Minimal Decompositions of Partially Ordered Sets into Chains.- XIII. Various Applications.- 1. A Sequencing Problem.- 2. Time-Table Scheduling (by Ivo Rosenberg).- 3. Applications to Coding Theory.- 4. Miscellanies.- 5. Plant Location.- 6. Other Types of Applications.- XIV. Minimization Problems in Automata Theory.- 1. Minimization of Normal Forms of Boolean Functions; Generalizations.- 2. Minimization of the Number of States m Input-Restricted Machines (by Ivo Rosenberg).- 3. The State Assignment of Sequential Circuits with High Reliability.- 4. Program Segmentation.- Appendix: Generalized Pseudo-Boolean Programming, by Ivo Rosenberg.- Conclusions.- Supplementary Bibliographies.- A. Boolean Equations and Generalizations.- B. Books on Boolean Algebra and Switching Theory.- Author Index.

(Produktform)Paperback / softback

(Zielgruppe)Fachpublikum/ Wissenschaft

(Zielgruppe)Research

Class number

Book number

P.L. Hammer ; S. Rudeanu

P L Hammer

R Bellmann

S Rudeanu

Electronic name

[Book]

Y