Average-Case Intractable NP Problems

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

A chapter in Advances in Algorithms, Languages, and Complexity, 1997, pp 313-378 from Springer

Abstract: 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.

Keywords: Turing Machine; Binary String; Hamiltonian Path; Positive Instance; Correspondence Problem (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3394-4_15

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DOI: 10.1007/978-1-4613-3394-4_15

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