Improved lower bounds for the randomized Boppana-Halldórsson algorithm for MAXCLIQUE

Abstract

It is shown that the randomized version of the Maxclique approximation algorithm by Boppana and Halldórsson analyzed in [5] does not come to within a factor of ${n \mathord{\left/{\vphantom {n {e^{3\sqrt {ln n} \ln \ln n} }}} \right.\kern-\nulldelimiterspace} {e^{3\sqrt {ln n} \ln \ln n} }}$ of the maximum clique. The lower bound derived in [5] was $\sqrt n$. Furthermore, we show that the randomized greedy algorithm for Maxclique does not come to within a factor of n/log^5+∈ n of the maximum clique. The lower bounds derived in this paper come close to the known upper bounds.