The importance of being biased

(MATH) We show that the Minimum Vertex Cover problem is NP-hard to approximate to within any factor smaller than $10\sqrt{5}-21 \approx 1.36067$, improving on the previously known hardness result for a $\frac{7}{6}$ factor.

[1]  P. Erdös,et al.  Intersection Theorems for Systems of Sets , 1960 .

[2]  Ran Raz,et al.  A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP , 1997, STOC '97.

[3]  Philip N. Klein,et al.  Approximation Algorithms for Steiner and Directed Multicuts , 1997, J. Algorithms.

[4]  Gil Kalai,et al.  Threshold Intervals under Group Symmetries , 1998 .

[5]  G. Kalai,et al.  Every monotone graph property has a sharp threshold , 1996 .

[6]  Eran Halperin,et al.  Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs , 2000, SODA '00.

[7]  Carsten Lund,et al.  Proof verification and the intractability of approximation problems , 1992, FOCS 1992.

[8]  Rudolf Ahlswede,et al.  The Complete Intersection Theorem for Systems of Finite Sets , 1997, Eur. J. Comb..

[9]  Ran Raz,et al.  A parallel repetition theorem , 1995, STOC '95.

[10]  Nathan Linial,et al.  Collective Coin Flipping , 1989, Adv. Comput. Res..

[11]  Carsten Lund,et al.  Proof verification and the hardness of approximation problems , 1998, JACM.

[12]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[13]  AhlswedeRudolf,et al.  The Complete Intersection Theorem for Systems of Finite Sets , 1997 .

[14]  L. Russo.  An approximate zero-one law , 1982 .

[15]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[16]  Sanjeev Arora,et al.  Probabilistic checking of proofs; a new characterization of NP , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[17]  Nathan Linial,et al.  The influence of variables on Boolean functions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[18]  Johan Håstad,et al.  Some optimal inapproximability results , 1997, STOC '97.

[19]  Reuven Bar-Yehuda,et al.  A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem , 1983, WG.

[20]  Ewald Speckenmeyer,et al.  Some Further Approximation Algorithms for the Vertex Cover Problem , 1983, CAAP.

[21]  I. Benjamini,et al.  Noise sensitivity of Boolean functions and applications to percolation , 1998 .

[22]  Manuel Blum,et al.  Self-testing/correcting with applications to numerical problems , 1990, STOC '90.

[23]  Mihir Bellare,et al.  Free Bits, PCPs, and Nonapproximability-Towards Tight Results , 1998, SIAM J. Comput..

[24]  Richard M. Wilson,et al.  The exact bound in the Erdös-Ko-Rado theorem , 1984, Comb..

[25]  J. Håstad.  Clique is hard to approximate within n 1-C , 1996 .

[26]  Jonas Holmerin,et al.  Clique Is Hard to Approximate within n1-o(1) , 2000, ICALP.

[27]  Luca Trevisan,et al.  Non-approximability results for optimization problems on bounded degree instances , 2001, STOC '01.

[28]  Subhash Khot,et al.  Improved inapproximability results for MaxClique, chromatic number and approximate graph coloring , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[29]  J. Spencer.  Intersection Theorems for Systems of Sets , 1977, Canadian Mathematical Bulletin.

[30]  Gyula O. H. Katona,et al.  Intersection theorems for systems of finite sets , 1964 .

[31]  Ehud Friedgut,et al.  Boolean Functions With Low Average Sensitivity Depend On Few Coordinates , 1998, Comb..