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Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems. In this paper, our aim is to investigate how these two fields can be combined to achieve better algorithms than what any of the two theories could offer. We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type, and propose directions for future research.doi:10.1093/comjnl/bxm048 fatcat:6yukdt7tvja3jf76zyuxfm536q