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Average-Case Intractable NP Problems

In: Advances in Algorithms, Languages, and Complexity

Author

Listed:
  • Jie Wang

    (University of North Carolina at Greensboro, Department of Mathematical Sciences)

Abstract

The notion of NP-completeness has provided a rigorous mathematical definition for measuring intractability of NP problems. But this measure applies only to worst-case complexity. Being NP-complete does not indicate that a problem is intractable on the average case. Indeed, some NP-complete problems are “easy on average,” though some may not be. Levin [39] initiated the study of average-case NP-completeness to measure average-case intractability. He showed that a bounded tiling problem under a simple distribution is average-case NP-complete. Since then, several additional average-case NP-complete problems have been shown within Levin’s framework. This paper is intended to provide a comprehensive survey of average-case NP-complete problems that have been published so far, and the techniques of obtaining these results.

Suggested Citation

  • Jie Wang, 1997. "Average-Case Intractable NP Problems," Springer Books, in: Ding-Zhu Du & Ker-I Ko (ed.), Advances in Algorithms, Languages, and Complexity, pages 313-378, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3394-4_15
    DOI: 10.1007/978-1-4613-3394-4_15
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