On independent sets in random graphs

SODA '11: 22nd ACM-SIAM Symposium on Discrete Algorithms San Francisco California January, 2011, pp. 436-486, 2015.

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random graphn lnsampling independents setindependent set problemphase transitions.More(12+)

Abstract:

The independence number of a sparse random graph G(n, m) of average degree d = 2m/n is well-known to be α(G(n, m)) ~ 2n ln(d)/d with high probability. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size (1 + o(1)) · n ln(d)/d, i.e., half the maximum size. Yet in spite of 30 years of extensive research no efficient...More

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