Algebraic and Combinatorial Methods in Operations Research

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R.E. Burkard, R.A. Cuninghame-Green, U. Zimmermann
Elsevier, Jan 1, 1984 - Mathematics - 380 pages
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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.

 

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Contents

Chapter 1 Packing problems in semigroup programming
1
Chapter 2 A greedy algorithm for solving network flow problems in trees
23
Chapter 3 A dual optimality criterion for algebraic linear programs
35
Chapter 4 On properties of solution sets of extremal linear programs
41
Chapter 5 Using fields for semiring computations
55
Chapter 6 Scheduling by noncommutative algebra
75
Chapter 7 Pseudoboolean functions and stability of graphs
83
Chapter 8 Independence systems and perfect kmatroidintersections
99
a survey of recent results
147
Chapter 13 Algebraic flows and timecost tradeoff problems
165
Chapter 14 Ranking the cuts and cutsets of a network
183
Chapter 15 Shortest paths in signed graphs
201
Chapter 16 A boolean algebraic analysis of fire protection
215
Chapter 17 Iteration and summability in semirings
229
Chapter 18 Substitution decomposition for discrete structures and connections with combinatorial optimization
257
Chapter 19 On maxseparable optimization problems
357

Chapter 9 Matroids on ordered sets and the greedy algorithm
115
Chapter 10 An algorithm for the unbounded matroid intersection polyhedron
129
Chapter 11 Algebraic Flows
135
Chapter 20 Minimization of combined objective functions on integral submolar flows
363
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