Author | Grรถtschel, Martin. author |
---|---|
Title | Geometric Algorithms and Combinatorial Optimization [electronic resource] / by Martin Grรถtschel, Lรกszlรณ Lovรกsz, Alexander Schrijver |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1993 |
Edition | Second Corrected Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-78240-4 |
Descript | XII, 362 p. online resource |
0. Mathematical Preliminaries -- 0.1 Linear Algebra and Linear Programming -- 0.2 Graph Theory -- 1. Complexity, Oracles, and Numerical Computation -- 1.1 Complexity Theory: P and NP -- 1.2 Oracles -- 1.3 Approximation and Computation of Numbers -- 1.4 Pivoting and Related Procedures -- 2. Algorithmic Aspects of Convex Sets: Formulation of the Problems -- 2.1 Basic Algorithmic Problems for Convex Sets -- 2.2 Nondeterministic Decision Problems for Convex Sets -- 3. The Ellipsoid Method -- 3.1 Geometric Background and an Informal Description -- 3.2 The Central-Cut Ellipsoid Method -- 3.3 The Shallow-Cut Ellipsoid Method -- 4. Algorithms for Convex Bodies -- 4.1 Summary of Results -- 4.2 Optimization from Separation -- 4.3 Optimization from Membership -- 4.4 Equivalence of the Basic Problems -- 4.5 Some Negative Results -- 4.6 Further Algorithmic Problems for Convex Bodies -- 4.7 Operations on Convex Bodies -- 5. Diophantine Approximation and Basis Reduction -- 5.1 Continued Fractions -- 5.2 Simultaneous Diophantine Approximation: Formulation of the Problems -- 5.3 Basis Reduction in Lattices -- 5.4 More on Lattice Algorithms -- 6. Rational Polyhedra -- 6.1 Optimization over Polyhedra: A Preview -- 6.2 Complexity of Rational Polyhedra -- 6.3 Weak and Strong Problems -- 6.4 Equivalence of Strong Optimization and Separation -- 6.5 Further Problems for Polyhedra -- 6.6 Strongly Polynomial Algorithms -- 6.7 Integer Programming in Bounded Dimension -- 7. Combinatorial Optimization: Some Basic Examples -- 7.1 Flows and Cuts -- 7.2 Arborescences -- 7.3 Matching -- 7.4 Edge Coloring -- 7.5 Matroids -- 7.6 Subset Sums -- 7.7 Concluding Remarks -- 8. Combinatorial Optimization: A Tour dโHorizon -- 8.1 Blocking Hypergraphs and Polyhedra -- 8.2 Problems on Bipartite Graphs -- 8.3 Flows, Paths, Chains, and Cuts -- 8.4 Trees, Branchings, and Rooted and Directed Cuts -- 8.5 Matchings, Odd Cuts, and Generalizations -- 8.6 Multicommodity Flows -- 9. Stable Sets in Graphs -- 9.1 Odd Circuit Constraints and t-Perfect Graphs -- 9.2 Clique Constraints and Perfect Graphs -- 9.3 Orthonormal Representations -- 9.4 Coloring Perfect Graphs -- 9.5 More Algorithmic Results on Stable Sets -- 10. Submodular Functions -- 10.1 Submodular Functions and Polymatroids -- 10.2 Algorithms for Polymatroids and Submodular Functions -- 10.3 Submodular Functions on Lattice, Intersecting, and Crossing Families -- 10.4 Odd Submodular Function Minimization and Extensions -- References -- Notation Index -- Author Index