Approximation Algorithms

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Springer Science & Business Media, 14.03.2013 - 380 Seiten
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Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell (1872-1970) Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed con jecture that P -=/= NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of ap proximation algorithms as it stands today. It is reasonable to expect the picture to change with time. This book is divided into three parts. In Part I we cover combinato rial algorithms for a number of important problems, using a wide variety of algorithm design techniques. The latter may give Part I a non-cohesive appearance. However, this is to be expected - nature is very rich, and we cannot expect a few tricks to help solve the diverse collection of NP-hard problems. Indeed, in this part, we have purposely refrained from tightly cat egorizing algorithmic techniques so as not to trivialize matters. Instead, we have attempted to capture, as accurately as possible, the individual character of each problem, and point out connections between problems and algorithms for solving them.
 

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Inhalt

Introduction
1
Other Topics
7
Steiner Tree and TSP
27
Notes
46
kCenter
47
Feedback Vertex Set
54
Shortest Superstring
61
Notes
67
12
93
Multicut and Integer Multicommodity Flow in Trees
145
Multiway Cut
154
Multicut in General Graphs
167
Sparsest Cut
179
A An Overview of Complexity Theory
344
B Basic Facts from Probability Theory
353
Problem Index
373

Bin Packing
74
Euclidean TSP
84

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