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Greedoids de Bernhard Korte

Greedoids: Algorithms and Combinatorics, cartea 4

Autor Bernhard Korte, Laszlo Lovasz, Rainer Schrader
en Limba Engleză Paperback – 18 oct 2012

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Specificații

ISBN-13: 9783642634994
ISBN-10: 3642634990
Pagini: 228
Ilustrații: VIII, 214 p.
Dimensiuni: 170 x 242 x 12 mm
Greutate: 0.37 kg
Ediția:Softcover reprint of the original 1st ed. 1991
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Algorithms and Combinatorics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

I. Introduction.- 1. Set Systems and Languages.- 2. Graphs, Partially Ordered Sets and Lattices.- II. Abstract Linear Dependence — Matroids.- 1. Matroid Axiomatizations.- 2. Matroids and Optimization.- 3. Operations on Matroids.- 4. Submodular Functions and Polymatroids.- III. Abstract Convexity — Antimatroids.- 1. Convex Geometries and Shelling Processes.- 2. Examples of Antimatroids.- 3. Circuits and Paths.- 4. Helly’s Theorem and Relatives.- 5. Ramsey-type Results.- 6. Representations of Antimatroids.- IV. General Exchange Structures — Greedoids.- 1. Basic Facts.- 2. Examples of Greedoids.- V. Structural Properties.- 1. Rank Function.- 2. Closure Operators.- 3. Rank and Closure Feasibility.- 4. Minors and Extensions.- 5. Interval Greedoids.- VI. Further Structural Properties.- 1. Lattices Associated with Greedoids.- 2. Connectivity in Greedoids.- VII. Local Poset Greedoids.- 1. Polymatroid Greedoids.- 2. Local Properties of Local Poset Greedoids.- 3. Excluded Minors for Local Posets.- 4. Paths in Local Poset Greedoids.- 5. Excluded Minors for Undirected Branchings Greedoids.- VIII. Greedoids on Partially Ordered Sets.- 1. Supermatroids.- 2. Ordered Geometries.- 3. Characterization of Ordered Geometries.- 4. Minimal and Maximal Ordered Geometries.- IX. Intersection, Slimming and Trimming.- 1. Intersections of Greedoids and Antimatroids.- 2. The Meet of a Matroid and an Antimatroid.- 3. Balanced Interval Greedoids.- 4. Exchange Systems and Gauss Greedoids.- X. Transposition Greedoids.- 1. The Transposition Property.- 2. Applications of the Transposition Property.- 3. Simplicial Elimination.- XI. Optimization in Greedoids.- 1. General Objective Functions.- 2. Linear Functions.- 3. Polyhedral Descriptions.- 4. Transversals and Partial Transversals.- 5.Intersection of Supermatroids.- XII. Topological Results for Greedoids.- 1. A Brief Review of Topological Prerequisites.- 2. Shellability of Greedoids and the Partial Tutte Polynomial.- 3. Homotopy Properties of Greedoids.- References.- Notation Index.- Author Index.- Inclusion Chart (inside the back cover).