Simple parallel and distributed algorithms for spectral graph sparsification

摘要

We describe a simple algorithm for spectral graph sparsification, based oniterative computations of weighted spanners and uniform sampling. Leveragingthe algorithms of Baswana and Sen for computing spanners, we obtain the firstdistributed spectral sparsification algorithm. We also obtain a parallelalgorithm with improved work and time guarantees. Combining this algorithm withthe parallel framework of Peng and Spielman for solving symmetric diagonallydominant linear systems, we get a parallel solver which is much closer to beingpractical and significantly more efficient in terms of the total work.