Hard Instances of Hard Problems

  • Authors:
  • Jack H. Lutz;Vikram Mhetre;Sridhar Srinivasan

  • Affiliations:
  • -;-;-

  • Venue:
  • STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
  • Year:
  • 2000

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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.