Overview

Oh cieca cupidigia, oh ira folie, Che si ci sproni nella vita corta, E nell' eterna poi si mal c'immolle! o blind greediness and foolish rage, That in our fleeting life so goads us on And plunges us in boiling blood for ever! Dante, The Divine Comedy Inferno, XII, 17, 49/51. On an afternoon hike during the second Oberwolfach conference on Mathematical Programming in January 1981, two of the authors of this book discussed a paper by another two of the authors (Korte and Schrader [1981]) on approximation schemes for optimization problems over independence systems and matroids. They had noticed that in many proofs the hereditary property of independence systems and matroids is not needed: it is not required that every subset of a feasible set is again feasible. A much weaker property is sufficient, namely that every feasible set of cardinality k contains (at least) one feasible subset of cardinality k - 1. We called this property accessibility, and that was the starting point of our investigations on greedoids.

Full Product Details

Author:   Bernhard Korte ,  Laszlo Lovasz ,  Rainer Schrader
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1991
Volume:   4
Dimensions:   Width: 17.00cm , Height: 1.20cm , Length: 24.20cm
Weight:   0.401kg
ISBN:  

9783642634994

ISBN 10:   3642634990
Pages:   214
Publication Date:   18 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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).

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions