Algebraic and Combinatorial Methods in Operations Research
- R.E. Burkard
- R.A. Cuninghame-Green
- U. Zimmermann
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For the first time, this book unites different algebraic approaches for discrete optimization and operations research. The presentation of some fundamental directions of this new fast developing area shows the wide range of its applicability.
Specifically, the book contains contributions in the following fields: semigroup and semiring theory applied to combinatorial and integer programming, network flow theory in ordered algebraic structures, extremal optimization problems, decomposition principles for discrete structures, Boolean methods in graph theory and applications.
- Published: January 1984
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-87571-6
For researchers in discrete optimisation, this book is very important.
Table of ContentsForeword. Packing Problems in Semigroup Programming (J. Aráoz). A Greedy Algorithm for Solving Network Flow Problems in Trees (P. Brucker). A Dual Optimality Criterion for Algebraic Linear Programs (P. Brucker, W. Papenjohann and U. Zimmermann). On Properties of Solution Sets of Extremal Linear Programs (P. Butkovič). Using Fields for Semiring Computations (R.A. Cuninghame-Green). Scheduling by Non-Commutative Algebra (R.A. Cuninghame-Green and W.F. Borawitz). Pseudo-Boolean Functions and Stability of Graphs (C. Ebenegger, P.L. Hammer and D. de Werra). Independence Systems and Perfect k-Matroid Intersections (R. Euler). Matroids on Ordered Sets and The Greedy Algorithm (U. Faigle). An Algorithm for the Unbounded Matroid Intersection Polyhedron (A. Frank and E. Tardos). Algebraic Flows (A.M. Frieze). Linear Algebra in Dioids; A Survey of Recent Results (M. Gondran and M. Minoux). Algebraic Flows and Time-Cost Tradeoff Problems (H.W. Hamacher and S. Tufekci). Ranking the Cuts and Cut-Sets of a Network (H.W. Hamacher, J.-C. Picard and M. Queyranne). Shortest Paths in Signed Graphs (P. Hansen). A Boolean Algebraic Analysis of Fire Protection (B.L. Hulme A.W. Shiver and P.J. Slater). Iteration and Summability in Semirings (B. Mahr). Substitution Decomposition for Discrete Structures and Connections with Combinatorial Optimization (R.H. Möhring and F.J. Radermacher). On Max-Separable Optimization Problems (K. Zimmermann). Minimization of Combined Objective Functions on Integral Submodular Flows (U. Zimmermann).