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Many of the computational problems that arise in practice are optimization problems: the task is to find a solution where the cost, quality, size, profit, or some other measure is as large or small as possible. The NP-hardness of an optimization problem implies that, unless P = NP, there is no polynomial-time algorithm that finds the exact value of the optimum. Various approaches have been proposed in the literature to cope with NP-hard problems. When designing approximation algorithms, we relax the requirement that the algorithm produces an optimum solution, and our aim is to devise a polynomial-time algorithm such that the solution it produces is not necessarily optimal, but there is some worst-case bound on the solution quality.
@InProceedings{demaine_et_al:DagSemProc.09511.2,
author = {Demaine, Erik D. and Hajiaghayi, MohammadTaghi and Marx, D\'{a}niel},
title = {{09511 Executive Summary – Parameterized complexity and approximation algorithms}},
booktitle = {Parameterized complexity and approximation algorithms},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2010},
volume = {9511},
editor = {Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.2},
URN = {urn:nbn:de:0030-drops-25011},
doi = {10.4230/DagSemProc.09511.2},
annote = {Keywords: Parameterized complexity, Approximation algorithms}
}