Linear degree extractors and the inapproximability of max clique and chromatic number

: We derandomize results of H?astad (1999) and Feige and Kilian (1998) and show that for all > 0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1are NP-hard. We further derandomize results of Khot (FOCS '01) and show that for some > 0, no quasi-polynomial time algorithm approximates MAX CLIQUE or CHROMATIC NUMBER to within n/2(logn)1, unless N~P = ~P. The key to these results is a new construction of dispersers, which are related to randomness extractors. A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log2 n + O(1) additional random bits for sources with constant entropy rate, and have constant error. Our dispersers use an arbitrarily small constant Most of this work was done while visiting Harvard University, and was supported in part by a Radcliffe Institute for Advanced Study Fellowship, a John Simon Guggenheim Memorial Fo...

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: David Zuckerman
• Keywords: Algorithms, John Simon Guggenheim, Lucile Packard Fel, Memorial Foundation Fellowship, STOC 2006