Greedoids (Algorithms and Combinatorics) 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024


Greedoids (Algorithms and Combinatorics)

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B. H. Korte 作者
Springer
譯者
1991-10 出版日期
0 頁數
USD 135.00 價格
Hardcover
叢書系列
9780387181905 圖書編碼

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Greedoids (Algorithms and Combinatorics) 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

Greedoids (Algorithms and Combinatorics) 在線電子書 epub 下載 pdf 下載 mobi 下載 txt 下載 2024

Greedoids (Algorithms and Combinatorics) 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024



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Greedoids (Algorithms and Combinatorics) 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

Greedoids (Algorithms and Combinatorics) 在線電子書 圖書描述

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 theroy and extending them to greedoids. It then proceeds to the discussion of subclasses like interval greedoids, antimatroids or convex geometries, greedoids on partically 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.

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