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Titlebook: Approximation Algorithms; Vijay V. Vazirani Book 2003 Springer-Verlag Berlin Heidelberg 2003 Approximation algorithms.Combinatorial optimi

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发表于 2025-3-21 18:31:42 | 显示全部楼层 |阅读模式
期刊全称Approximation Algorithms
影响因子2023Vijay V. Vazirani
视频video
发行地址Spreads powerful algorithmic ideas developed in this area to practitioners.Will accelerate progress in this area.Raises algorithmic awareness of the scientific community by showing simple ways of expr
图书封面Titlebook: Approximation Algorithms;  Vijay V. Vazirani Book 2003 Springer-Verlag Berlin Heidelberg 2003 Approximation algorithms.Combinatorial optimi
影响因子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
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s of the scientific community by showing simple ways of exprAlthough 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,
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https://doi.org/10.1007/978-3-8350-9498-7on 2.1 we deferred giving the lower bounding method on which this algorithm was based. We will provide the answer below. The power of this approach will become apparent when we show the ease with which it extends to solving several generalizations of the set cover problem (see Section 13.2).
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Steiner Tree and TSP case. For TSP, without this restriction, the problem admits no approximation factor, assuming . ≠ .. The algorithms, and their analyses, are similar in spirit, which is the reason for presenting these problems together.
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-Centerr the restriction that the edge costs satisfy the triangle inequality. Without this restriction, the .-center problem cannot be approximated within factor .(.), for any computable function .(.), assuming . ≠ . (see Exercise 5.1).
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