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Greedoids

Bibliographic Details
Main Authors: Korte, Bernhard, Lovasz, Laszlo (Author), Schrader, Rainer (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1991, 1991
Edition:1st ed. 1991
Series:Algorithms and Combinatorics
Subjects:
Discrete Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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)
  • 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
  • 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

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