Title: The Parsimonious Property of Cut Covering Problems and Its Applications January, 1994 Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 1332274277
ISBN 13: 9781332274277
Binding: PAP
Condition: New

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Synopsis

This book provides an in-depth analysis of the "parsimonious" property of cut covering problems, a class of combinatorial challenges that encompass well-known issues like the Steiner tree and traveling salesman conundrums. The author initially presents a set of conditions that, when met by a set function, will guarantee the parsimonious property. This property implies that degree constraints in the linear programming relaxation of cut covering problems can be omitted without affecting the optimal solution, an observation that has spurred significant advancements in the field. The author continues by examining various implications of this property, including monotonicity properties of the linear programming relaxation and the integrality of polyhedra associated with these problems. In doing so, this book unifies and expands upon several previously independent results, revealing the underlying connections between them. Additionally, the author proposes new methods for analyzing the worst-case performance of approximation algorithms for cut covering problems and introduces a novel approximation algorithm that is simpler to implement than existing methods. This book provides a comprehensive understanding of the parsimonious property and its significance in addressing cut covering problems, offering valuable insights for researchers and practitioners working in combinatorial optimization and related areas.

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