U. Feige, "Randomized Graph Products, Chromatic Numbers, and the Lov'asz `- Function", in Proc. 27th Annual ACM Symposium on Theory of Computing, 1995, pp. 635--640. Home/Search Document Details and Download
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Around the PCP Theorem - Arora (1997) (Correct)
....Zachos [BoHaZa] If Graph Isomorphism is NP complete, then the polynomial time hierarchy collapses to Sigma P 2 =BP DeltaNP. See also [Scho] and [KST] Actually the above proof method works not only for Graph Isomorphism, more generally it can be shown: Goldwasser, Sipser [GoSi] IP[2] AM[4]. Proof: In a two round (private coin) protocol, on input x, the Verifier V picks a random number r, computes q = q(x#r) and sends q to the Prover. The Prover selects an answer a such that the probability that the Verifier afterwards accepts, i.e. q(x#r#a) accept, is maximized. By some lower ....
....137 (1995) 279 282. 2] L. Babai. Trading group theory for randomness. 17th ACM Symp. Theory of Computing 1985, 421 429. 3] L. Babai, S. Moran. Arthur Merlin games: a randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences 36 (1988) 254 276. [4] T. Baker, A.L. Selman. A second step toward the polynomial hierarchy. Theoretical Computer Science 8 (1979) 177 187. 5] J. Balc azar. Self reducibility structures and solutions of NP problems. Revista Mathematica, 175 184, Universidad Complutense de Madrid (1989) 6] C.H. Bennett, J. Gill. ....
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U. Feige, "Randomized graph products, chromatic numbers and the Lovasz `- function", Proc. 27th ACM Symp. on Theory of Computing (1995) 635-640.
The Lovasz Theta Function and a Semidefinite Programming.. - Kleinberg, Goemans (1995) (16 citations) (Correct)
....vc(G) and n Gamma #(G) can also be obtained from a construction due independently to Alon and Kahale [1] their concern was with the complement of our problem: graphs G with small independence number for which #(G) converges to 1 2 n. We also note that the recent construction of Feige [4], showing that the ratio #(G) ff(G) can be as large as n 1 Gammao(1) is of no use for our purposes; for the graphs he deals with, the ratio of vc(G) to n Gamma #(G) converges to 1, not 2. In the final section we present a natural strengthening of the formulation; this turns out to be equal ....
U. Feige, "Randomized graph products, chromatic numbers, and the Lov'asz `- function," Proc. 27th ACM Symposium on Theory of Computing, 1995.
On the Densest K-Subgraph Problem - Feige, Seltser (1997) (1 citation) Self-citation (Feige) (Correct)
....of fundamental problems [12, 16, 7, 9, 2] In all above applications of SP, the authors also studied the limitations of the SP approach, and showed that the particular SP formulations that they use do not in fact give approximation ratios that are significantly better than those proved. See also [6]. All the new developments mentioned above are randomized algorithms. All of them share the following common paradigm. First, a semidefinite program is solved to obtain Y as defined in (I) Then Y which is a Gram matrix is decomposed (using Incomplete Cholesky Decomposition [12] to a collection ....
U. Feige, "Randomized Graph Products, Chromatic Numbers, and the Lov'asz `- Function", in Proc. 27th Annual ACM Symposium on Theory of Computing, 1995, pp. 635--640.
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