Skip to main content
Article thumbnail
Location of Repository

Improved spectral sparsification and numerical algorithms for sdd matrices

By Ioannis Koutis, Alex Levin and Richard Peng

Abstract

We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/ɛ 2) edges that provides a strong approximation of G. Namely, for all vectors x and any ɛ> 0, we have (1 − ɛ)x T LGx ≤ x T LHx ≤ (1 + ɛ)x T LGx, where LG and LH are the Laplacians of the two graphs. The first algorithm is a simple modification of the fastest known algorithm and runs in Õ(m log2 n) time, an O(log n) factor faster than before. The second algorithm runs in Õ(m log n) time and generates a sparsifier with Õ(n log3 n) edges. The third algorithm applies to graphs where m> n log 5 n and runs in Õ(m logm/n log5 n n) time. In the range where m> n1+r for some constant r this becomes Õ(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing fundamental eigenvectors of dense SDD matrices

Topics: linear system solving
Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.9713
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.cs.cmu.edu/~jkoutis... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.