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APPROX
2009
Springer

Random Tensors and Planted Cliques

10 years 8 months ago
Random Tensors and Planted Cliques
The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor’s entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r = 2, it is the adjacency matrix with 1’s for edges and −1’s for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O( √ n). Here we show that the 2-norm of the r-parity tensor is at most f(r) √ n logO(r) n, answering a question of Frieze and Kannan [3] who proved this for r = 3. As a consequence, we get a tight connection between the planted clique problem and the problem of finding a vector that approximates the 2-norm of the r-parity tensor of a random graph. Our proof method is based on an inductive application of concentration of measure.
S. Charles Brubaker, Santosh Vempala
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Where APPROX
Authors S. Charles Brubaker, Santosh Vempala
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