A Matrix Hyperbolic Cosine Algorithm and Applications

  • Anastasios Zouzias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


In this paper, we generalize Spencer’s hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which the matrices have a group structure and an other in which they have rank-one. As an application of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, it constructs an expanding Cayley graph of logarithmic degree in near-optimal \(\mathcal{O}(n^2\log^3 n)\) time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices, which implies an improved deterministic algorithm for spectral graph sparsification of dense graphs. In addition, we give an elementary connection between spectral sparsification of positive semi-definite matrices and element-wise matrix sparsification. As a consequence, we obtain improved element-wise sparsification algorithms for diagonally dominant-like matrices.


Cayley Graph Symmetric Matrice Deterministic Algorithm Dense Graph Fast Multipole Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anastasios Zouzias
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoCanada

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