Greedoids - neues Buch

EAN (ISBN-13): 9783642581915
Erscheinungsjahr: 2012
Herausgeber: Springer Berlin Heidelberg

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ISBN/EAN: 9783642581915

ISBN - alternative Schreibweisen:
978-3-642-58191-5
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: bernhard korte, schrader, shibatani masayoshi

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Daten vom Verlag:

Autor/in: Bernhard Korte; Laszlo Lovasz; Rainer Schrader
Titel: Algorithms and Combinatorics; Greedoids - Study and Research Texts
Verlag: Springer; Springer Berlin
214 Seiten
Erscheinungsjahr: 2012-12-06
Berlin; Heidelberg; DE
Sprache: Englisch
53,49 € (DE)
55,00 € (AT)
59,00 CHF (CH)
Available
VIII, 214 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Sonstiges; Diskrete Mathematik; Verstehen; Lattice; algorithms; boundary element method; combinatorial optimization; computer; design; discrete mathematics; function; graphs; mathematical programming; mathematics; matroid; object; optimization; proof; combinatorics; C; Discrete Mathematics; Mathematics and Statistics; BC

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).