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/log5+∈ n of the maximum clique. The lower bounds derived in this paper come close to the known upper bounds.
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References
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© 1995 Springer-Verlag Berlin Heidelberg
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Peinado, M. (1995). Improved lower bounds for the randomized Boppana-Halldórsson algorithm for MAXCLIQUE. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030876
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DOI: https://doi.org/10.1007/BFb0030876
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