Abstract
This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows that every weakly hard problem has a dense set of such maximally hard instances. This extends the theorem, due to Orponen, Ko, Schöning and Watanabe (1994), that every hard problem for exponential time has a dense set of maximally hard instances. Complementing this, it is shown that every hard problem for exponential time also has a dense set of unusually easy instances.
This research was supported in part by National Science Foundation Grant CCR9610461.
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Lutz, J.H., Mhetre, V., Srinivasan, S. (2000). Hard Instances of Hard Problems. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_27
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DOI: https://doi.org/10.1007/3-540-46541-3_27
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