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Are there any known "hard" instances for NP-Complete Problems,

or are there no general hard instances. So for different algorithms different instances are hard?

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closed as unclear what you're asking by D.W., Pål GD, Luke Mathieson, David Richerby, Rick Decker Feb 19 '15 at 1:56

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    $\begingroup$ ... where "hard" means an NP-hard distribution or that there is no known polynomial-time algorithm for the distribution? $\;$ $\endgroup$ – user12859 Feb 18 '15 at 16:49
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    $\begingroup$ No single instance can be hard, since it is hard-coded. There could be an infinite sequence of instances which is hard in the sense that if some polytime algorithm works correctly on all of them, then P=NP. The set of all instances is such an example, but sometimes smaller sets also work. $\endgroup$ – Yuval Filmus Feb 18 '15 at 17:28
  • $\begingroup$ and many instance can be trivially solved, but then there has to be a minimum set of the "hard" instances! But is there anything known, where these instances lie, how do they look like? $\endgroup$ – guest Feb 18 '15 at 17:48
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    $\begingroup$ Why does there have "to be a minimum set of the 'hard' instances"? $\;$ $\endgroup$ – user12859 Feb 18 '15 at 18:30
  • $\begingroup$ Wouldn't otherwise all instance be easy? $\endgroup$ – guest Feb 18 '15 at 18:33

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