Hard Graphs for the Randomized Boppana-Halldörsson Algorithm for MAXCLIQUE

A randomized version of the MAXCLIQUE approximation algorithm by Boppana and Halldorsson is analyzed. The Boppana Halldorsson algorithm has the best performance guarantee currently known for the MAXCLIQUE problem. This paper presents a class of graphs on which the performance ratio of the randomized version of the algorithm is not better than Ω(√n) with probability greater than 1 - 1/nω(1).

[1]  Torben Hagerup,et al.  A Guided Tour of Chernoff Bounds , 1990, Inf. Process. Lett..

[2]  Peter Frankl,et al.  Intersection theorems with geometric consequences , 1981, Comb..

[3]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[4]  Mihir Bellare,et al.  Improved non-approximability results , 1994, STOC '94.

[5]  Ludek Kucera,et al.  The Greedy Coloring Is a Bad Probabilistic Algorithm , 1991, J. Algorithms.

[6]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[7]  Ravi B. Boppana,et al.  Approximating maximum independent sets by excluding subgraphs , 1990, BIT.

[8]  Mark Jerrum,et al.  Large Cliques Elude the Metropolis Process , 1992, Random Struct. Algorithms.

[9]  William I. Gasarch,et al.  On bounded queries and approximation , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.