This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. It offers a unifying approach which is based on two fundamental geometric algorithms: the ellipsoid method for finding a point in a convex set and the basis reduction method for point lattices. This book is a continuation and extension of previous research of the authors for which they received the Fulkerson prize, awarded by the Mathematical ...
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This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. It offers a unifying approach which is based on two fundamental geometric algorithms: the ellipsoid method for finding a point in a convex set and the basis reduction method for point lattices. This book is a continuation and extension of previous research of the authors for which they received the Fulkerson prize, awarded by the Mathematical Programming Society and the American Mathematical Society. The first edition of this book was received enthusiastically by the community of discrete mathematicians, combinatorial optimizers, operations researchers, and computer scientists. To quote just from a few reviews: "The book is written in a very grasping way, legible both for people who are interested in the most important results and for people who are interested in technical details and proofs." #"manuscripta geodaetica"#1
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Physical description: XII, 362p. 23 illus. Notes: Bibliographic Level Mode of Issuance: Monograph Includes bibliographical references and index. Contents: 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 d'Horizon--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. Subjects: Combinatorial geometry. Geometry of numbers. Mathematical optimization. Combinatorial geometry. Geometry of numbers. Mathematical optimization. Programming (Mathematics) Combinatorial geometry. Geometry of numbers. Mathematical optimization. Programming (Mathematics) Mathematics. Combinatorial analysis. Combinatorial analysis. Mathematics. Combinatorics. Library copy-library marks remain. Very good copy in the original title-blocked cloth. Slight suggestion only of dust-dulling to the spine bands and panel edges. Remains particularly well-preserved overall; tight, bright, clean and strong.
Add this copy of Geometric Algorithms and Combinatorial Optimization to cart. $169.51, new condition, Sold by Just one more Chapter rated 4.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2011 by Springer.
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Add this copy of Geometric Algorithms and Combinatorial Optimization to cart. $263.36, new condition, Sold by Just one more Chapter rated 4.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 1988 by Springer-Verlag.
