A Matrix Hyperbolic Cosine Algorithm and Applications

Wigderson and Xiao presented an efficient derandomization of the matrix Chernoff bound using the method of pessimistic estimators [WX08]. Building on their construction, we present a derandomization of the matrix Bernstein inequality which can be viewed as generalization of Spencer’s hyperbolic cosine algorithm [Spe77]. We apply our construction to several problems by analyzing its computational efficiency under two special cases of matrix samples; one in which the samples have a group structure and the other in which they have rank-one outer-product structure. As a consequence of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, constructs an Alon-Roichman expanding Cayley graph of logarithmic degree in O(n2 log3 n) time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semidefinite matrices (as defined in [Sri10]), which implies an improved deterministic...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Anastasios Zouzias
• Keywords: CORR 2011, Deterministic Algorithm, Education, Matrix, Spectral Sparsification