TY - JOUR
T1 - Finding a large hidden clique in a random graph
AU - Alon, Noga
AU - Krivelevich, Michael
AU - Sudakov, Benny
PY - 1998
Y1 - 1998
N2 - We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph G(n, 1/2), and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kučera. In this paper we present an efficient algorithm for all k > cn0.5, for any fixed c > 0, thus improving the trivial case k > cn0.5(log n)0.5. The algorithm is based on the spectral properties of the graph.
AB - We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph G(n, 1/2), and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kučera. In this paper we present an efficient algorithm for all k > cn0.5, for any fixed c > 0, thus improving the trivial case k > cn0.5(log n)0.5. The algorithm is based on the spectral properties of the graph.
UR - https://www.scopus.com/pages/publications/0032221884
U2 - 10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w
DO - 10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w
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AN - SCOPUS:0032221884
SN - 1042-9832
VL - 13
SP - 457
EP - 466
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
IS - 3-4
ER -