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Suppose the fastest algorithm that we can design for some problem runs in time O(n 2 ). However, we want to solve the problem on big data inputs, for which quadratic time is impractically slow. We can keep searching for a faster algorithm, but maybe none exists. Is there any reasoning that provides evidence against significantly faster algorithms, and thus allows us to stop searching? In other words, is there an analogue of NP-hardness for polynomial-time problems? In this tutorial, we willdoi:10.4230/lipics.stacs.2019.4 dblp:conf/stacs/Bringmann19 fatcat:ulgtwbxw3jctdkuh37lliq3jjy