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Abstract: Many recent results show the hardness of approximating NP-hard functions. We formalize, in a very simple way, what these results involve: a code-like Levin reduction. Assuming a well-known complexity assumption, we show that such reductions cannot prove the NP-hardness of the following problems, where e is any positive fraction: (i) achieving an approximation ratio n^(1/2+e) for Clique, (ii) achieving an approximation ratio 1.5 + e for Vertex Cover, and (iii) coloring a 3-colorable graph with... (Update)
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BibTeX entry: (Update)
S. Arora. "Reductions, codes, PCPs, and inapproximability". Proc. of 36th Annual Symposium of Foundations of Computer Science, 404--413, 1995. http://citeseer.ist.psu.edu/arora95reductions.html More
@inproceedings{ arora95reductions,
author = "Sanjeev Arora",
title = "Reductions, Codes, {PCPs}, and Inapproximability",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "404-413",
year = "1995",
url = "citeseer.ist.psu.edu/arora95reductions.html" }
Citations (may not include all citations):4212 Computers and Intractability: a guide to the theory of NPcom.. (context) - Garey, Johnson - 1979
773 Reducibility among combinatorial problems (context) - Karp - 1972
534 The complexity of theorem-proving procedures (context) - Cook - 1971
300 the hardness of approximating minimization problems (context) - Lund, Yannakakis - 1993
293 Approximation algorithms for combinatorial problems (context) - Johnson - 1974
212 Probabilistic checking of proofs: A new characterization of .. - Arora, Safra - 1992
203 Approximating clique is almost NP-complete (context) - Feige, Goldwasser et al. - 1991
173 Proof verification and intractability of approximation probl.. (context) - Arora, Lund et al. - 1992
163 NP is as easy as detecting unique solutions (context) - Valiant, Vazirani - 1986
155 Checking Computations in Polylogarithmic Time - Babai, Fortnow et al. - 1991
118 A parallel repetition theorem - Raz
108 Improved nonapproximability results - Bellare, Sudan - 1994
106 Matching is as easy as matrix inversion (context) - Mulmuley, Vazirani et al. - 1987
104 Approximating maximum independent sets by excluding subgraph.. - Boppana, Halld'orsson - 1992
103 Bounded Arithmetic (context) - Buss - 1986
[Article contains additional citations not shown here]
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