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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 [Lev86] initiated the study of average-case NP-completeness to measure average-case intractability. He showed that a bounded tiling problem ... (Update)
Context of citations to this paper: More
.... 5 C mon guys, you re laying it on a bit thick, aren t you For a more optimistic view on average case complexity, please consult [Wang97a, Wang97b]. EWA These seemed at first to be potentially powerful generalizations of polynomial time. Randomized Monte Carlo and Las Vegas...
.... need to construct a reduction that produces a witness along with the yes no answer, so that the correctness of the answer can be verified [Wan97]. 1. Average Case Computational Complexity Theory 19 following lemma for distributional decision problems. The lemma is also true for...
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BibTeX entry: (Update)
J. Wang. Average-case intractable NP problems. In D.-Z. Du and K.-I. Ko, editors, Advances in Languages, Algorithms, and Complexity, Kluwer Academic Publishers, pp. 313-378, 1997. http://citeseer.ist.psu.edu/253426.html More
@inproceedings{ wang97averagecase,
author = "Jie Wang",
title = "Average-Case Intractable {NP} Problems",
booktitle = "Advances in Algorithms, Languages, and Complexity",
pages = "313-378",
year = "1997",
url = "citeseer.ist.psu.edu/253426.html" }
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Documents on the same site (http://www.uncg.edu/~wangjie/recent_pub.html):
Average-case Computational Complexity Theory - Wang (1996) (Correct)
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