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Finding cliques using few probes

by   Uriel Feige, et al.
Princeton University
Weizmann Institute of Science
Georgia Institute of Technology

Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from G_n,1/2 (and hence is likely to have a clique of size roughly 2 n), then for every δ < 2 and constant ℓ, there is an α < 2 (that may depend on δ and ℓ) such that no algorithm that makes n^δ probes in ℓ rounds is likely (over the choice of the random graph) to output a clique of size larger than α n.


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