Probabilistically Checkable Proofs and Inapproximability
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Here is the tentative list of papers which we will partially cover in the class. It will be updated regularly


  1. I. Dinur, E. Fischer, R. Raz, G. Kindler, S. Safra, PCP Characterizations of NP: Towards a Polynomially-Small Error-Probability, STOC 1999

  2. S. Arora and S. Safra, Probabilistic Checking of Proofs: A New Characterization of NP, J. of the ACM, 45(1):70-122, 1998.

  3. M. Bellare, Proof Checking and Approximations: Towards Tight Results, Sigact News, 27(1): 1996 (nice survey, right in the middle of the events)

  4. J. Hastad, Some Optimal Inapproximability Results, J. of the ACM, 48(4):798-859, 2001

  5. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof Verification and Hardness of Approximation Problems, J. of the ACM, 45(3):501-555, 1998.

Interactive Proofs and Inapproximability

  1. U. Feige, S. Goldwasser, L. Lovasz, S. Safra, and M. Szegedy, Interactive Proofs and the Hardness of Approximating Cliques, J. of the ACM, 43(2):268-292, 1996

  2. C. Lund and M. Yannakakis, On the Hardness of Approximating Minimization Problems, J. of the ACM, 41:960:981, 1994

  3. J. Hastad, Clique is Hard to Approximate within $n^( 1 - \epsilon)$, Acta Matehmatica, 182:105-142, 1999

  4. U. Feige, A Threshold of $\ln n$ for Approximating Set Cover, J. of the ACM, 45(4):634-652, 1998

  5. M. Bellare,O. Goldreich, and M. Sudan, Free Bits, PCP's and Non-Approximability Towards Tight Results, SIAM J. on Computing, 27(3):804-915, 1998

  6. I. Dinur and S. Safra, On the Hardness of Approximating Minimum Vertex Cover

  7. U. Geige and J. Kilian, Zero Knowledge on the Chromatics Number, J. of Computer and System Sciences, 57(2), 187-199, 1998

  8. H. J. Karloff, U. Zwich, A 7/8-Approximation Algorithm for MAX 3SAT, FOCS 1997

  9. I. Dinur and S. Safra, The importance of Being Biased, STOC 2002

  10. J. Chuzhoy, On the Approximability of Some Network Design Problems, SODA 2007

  11. M. Andrews, J. Chuzhoy, S. Khanna, and L. Zhang, Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion, FOCS 2005

  12. M. Andrews and L. Zhang, Logarithmic Hardness of the Undirected Edge-Disjoint paths Problem, J. of the ACM, 53(5):745-761, 1006

  13. P. Crescenzi, R. Silvestri, and L. Trevisan, On Weighted vs. Unweighted Versions of Combinatorial Optimization Problems, Inf. Comput. 167(1):10-26, 2001

CIS 6930: PCPs and Inapproximablity