2011 | OriginalPaper | Chapter
New Multithreaded Ordering and Coloring Algorithms for Multicore Architectures
Authors : Md. Mostofa Ali Patwary, Assefaw H. Gebremedhin, Alex Pothen
Published in: Euro-Par 2011 Parallel Processing
Publisher: Springer Berlin Heidelberg
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We present new multithreaded vertex
ordering
and
distance-k graph coloring
algorithms that are well-suited for multicore platforms. The vertex ordering techniques rely on various notions of “degree”, are known to be effective in reducing the number of colors used by a
greedy
coloring algorithm, and are generic enough to be applicable to contexts other than coloring. We employ
approximate degree
computation in the ordering algorithms and
speculation
and
iteration
in the coloring algorithms as our primary tools for breaking sequentiality and achieving effective parallelization. The algorithms have been implemented using OpenMP, and experiments conducted on Intel Nehalem and other multi-core machines using various types of graphs attest that the algorithms provide scalable runtime performance. The number of colors the algorithms use is often close to optimal. The techniques used for computing the ordering and coloring in parallel are applicable to other problems where there is an inherent ordering to the computations that needs to be relaxed for increasing concurrency.