DagSemProc.09511.2.pdf
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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.
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