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Parallel Graph Coloring for Manycore Architectures

Proceedings - 2016 IEEE 30th International Parallel and Distributed Processing Symposium, IPDPS 2016

Deveci, Mehmet D.; Boman, Erik G.; Devine, Karen D.; Rajamanickam, Sivasankaran R.

Graph algorithms are challenging to parallelize on manycore architectures due to complex data dependencies and irregular memory access. We consider the well studied problem of coloring the vertices of a graph. In many applications it is important to compute a coloring with few colors in near-lineartime. In parallel, the optimistic (speculative) coloring method by Gebremedhin and Manne is the preferred approach but it needs to be modified for manycore architectures. We discuss a range of implementation issues for this vertex-based optimistic approach. We also propose a novel edge-based optimistic approach that has more parallelism and is better suited to GPUs. We study the performance empirically on two architectures(Xeon Phi and GPU) and across many data sets (from finite element problems to social networks). Our implementation uses the Kokkos library, so it is portable across platforms. We show that on GPUs, we significantly reduce the number of colors (geometric mean 4X, but up to 48X) as compared to the widely used cuSPARSE library. In addition, our edge-based algorithm is 1.5 times faster on average than cuSPARSE, where it hasspeedups up to 139X on a circuit problem. We also show the effect of the coloring on a conjugate gradient solver using multi-colored Symmetric Gauss-Seidel method as preconditioner, the higher coloring quality found by the proposed methods reduces the overall solve time up to 33% compared to cuSPARSE.

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TYPE Conference Poster YEAR 2016
ScopusOSTI

An empirical comparison of graph laplacian solvers

Proceedings of the Workshop on Algorithm Engineering and Experiments

Boman, Erik G.; Deweese, Kevin; Gilbert, John R.

Solving Laplacian linear systems is an important task in a variety of practical and theoretical applications. This problem is known to have solutions that perform in linear times polylogarithmic work in theory, but these algorithms are difficult to implement in practice. We examine existing solution techniques in order to determine the best methods currently available and for which types of problems are they useful. We perform timing experiments using a variety of solvers on a variety of problems and present our results. We discover differing solver behavior between web graphs and a class of synthetic graphs designed to model them.

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TYPE Conference Poster YEAR 2016
ScopusOSTIDOI

Evaluating the Potential of a Laplacian Linear Solver

Boman, Erik G.; Deweese, Kevin D.; Gilbert, John R.

A new approach for solving Laplacian linear systems proposed by Kelner et al. involves the random sampling and update of fundamental cycles in a graph. We evaluate the performance of this approach on a variety of real world graphs. We examine di erent ways to choose the set of cycles and their sequence of updates with the goal of providing more exibility and potential parallelism. We propose a parallel model of the Kelner et al. method for evaluating potential parallelism concerned with minimizing the span of edges updated at every iteration. We provide experimental results comparing the potential parallelism of the fundamental cycle basis and the extended basis. Our preliminary experiments show that choosing a non-fundamental set of cycles can save signi cant work compared to a fundamental cycle basis.

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TYPE Journal Article YEAR 2015
OSTI
Results 76–100 of 210
Results 76–100 of 210