Ling Liu's SC13 paper "Large Graph Processing Without the Overhead" featured by HPCwire.
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Second GraphLab workshop should be even bigger than the first! GraphLab is a new programming framework for graph-style data analytics.
Nearly-Linear Work Parallel SDD Solvers, Low-Diameter Decomposition, and Low-Stretch Subgraphs
Theory of Computer Systems, Volume 55, Issue 3, October 2014.
Guy E. Blelloch*, Anupam Gupta*, Ioannis Koutis^, Gary L. Miller*, Richard Peng*,
* Carnegie Mellon University
^ University of Puerto Rico, Rio Piedras, Puerto Rico
We present the design and analysis of a nearly-linear work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input an SDD n-by-n matrix A with m nonzero entries and a vector b, our algorithm computes a vector ˜x such that ∥˜x − A + b ∥A ≤ ε · ∥A + b∥A in O(m logO(1) n log 1/ε ) work and
O(m1/3+θ log 1/ε ) depth for any θ > 0, where A+ denotes the Moore-Penrose pseudoinverse of A. The algorithm relies on a parallel algorithm for generating low-stretch spanning trees or spanning subgraphs. To this end, we first develop a parallel decomposition algorithm that in O(m logO(1)n) work and polylogarithmic depth, partitions a graph with n nodes and m edges into components with polylogarithmic diameter such that only a small fraction of the original edges are between the components. This can be used to generate low-stretch spanning trees with average stretch O(nα) in O(m logO(1) n) work and O(nα) depth for any α >0. Alternatively, it can be used to generate spanning subgraphs with polylogarithmic average stretch in O(mlogO(1) n) work and polylogarithmic depth. We apply this subgraph construction to derive a parallel linear solver.
By using this solver in known applications, our results imply improved parallel randomized algorithms for several problems, including single-source shortest paths, maximum flow, minimum-cost flow, and approximate maximum flow.
FULL PAPER: pdf