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Unformatted text preview: > 0, GAP-CLIQUE 1 , is NP-hard) using the powering graph (similar to the one we used to show the hardness of approximation of Independent Set). That is, for a graph G = ( V,E ) and an integer k 2, you need to dene the k th power of G , G k = ( V ,E ) such that ( G k ) = ( G ) k where ( . ) denes the size of largest cliques in (.). From there, prove the theorem. Problem 6 . Show that there exits a > 0, GAP-CLIQUE 1 ,n- is NP-hard. As hinted in the lecture note, you may want to choose k to be supper-constant, then the verier needs a total of O ( k log n )random bits, then the size of G becomes supper-polynomial. Try to show that we can run the verier k times by using only O (log n ) + O ( k ) (rather than O ( k log n ))...
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This note was uploaded on 05/20/2011 for the course CIS 6930 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08