Greedoids: Vol 4 (Algorithms and Combinatorics)

Korte, Bernhard (Author)/ Lovasz, Laszlo (Author)/ Schrader, Rainer (Author)

ISBN 10: 3540181903 / ISBN 13: 9783540181903

Published by Springer, 1991

About this Item

228 pages. 6.69x0.56x9.61 inches. In Stock. Seller Inventory # x-3540181903

Bibliographic Details

Title: Greedoids: Vol 4 (Algorithms and ...

Publisher: Springer

Publication Date: 1991

Binding: Hardcover

Condition: Brand New

About this title

Synopsis:

With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the underlying mathematical object, and properties exploited by algorithms are often closely tied to classical structural analysis in mathematics. This connection between algorithms and structure is in particular apparent in discrete mathematics, where proofs are often constructive, and can be turned into algorithms more directly. The principle of greediness plays a fundamental role both in the design of continuous algorithms (where it is called the steepest descent or gradient method) and of discrete algorithms. The discrete structure most closely related to greediness is a matroid; in fact, matroids may be characterized axiomatically as those independence systems for which the greedy solution is optimal for certain optimization problems (e.g. linear objective functions, bottleneck functions). This book is an attempt to unify different approaches and to lead the reader from fundamental results in matroid theory to the current borderline of open research problems. The monograph begins by reviewing classical concepts from matroid theory and extending them to greedoids. It then proceeds to the discussion of subclasses like interval greedoids, antimatroids or convex geometries, greedoids on partially ordered sets and greedoid intersections. Emphasis is placed on optimization problems in greedois. An algorithmic characterization of greedoids in terms of the greedy algorithm is derived, the behaviour with respect to linear functions is investigated, the shortest path problem for graphs is extended to a class of greedoids, linear descriptions of antimatroid polyhedra and complexity results are given and the Rado-Hall theorem on transversals is generalized. The self-contained volume which assumes only a basic familarity with combinatorial optimization ends with a chapter on topological results in connection with greedoids.

Synopsis:

This monograph attempts to unify different mathematical approaches and to lead the reader from fundamental results in matroid theory to the current state-of-the-art in open research problems. It reviews classical concepts from matroid theory and extends them to greedoids ("greedy" algorithms).