Constrained Fine-Grain Parallel Sparse Matrix Distribution
نویسندگان
چکیده
We consider how to distribute sparse matrices among processors to reduce communication cost in parallel sparse matrix computations, in particular, sparse matrix-vector multiplication. We allow 2d distributions, where the distribution (partitioning) is not constrained to just rows or columns. The fine-grain model is a 2d distribution introduced in [2] where nonzeros can be assigned to processors in an arbitrary general way. They proposed a hypergraph model and showed it can significantly reduce the communication volume compared to 1d distributions. We define a constrained version of this problem, where the input and output vector distributions are given. We propose two combinatorial models. The first is based on vertex cover in the bipartite graph, and the second on hypergraph partitioning with fixed vertices. Though NP-hard, both models can be solved heuristically using existing algorithms and software. Sparse matrix-vector multiplication is usually parallelized such that the processor that owns element aij computes the contribution aijxj . This is a local operation if xj , yi and aij all reside on the same processor; otherwise communication is required. In general, the following four steps are performed:
منابع مشابه
Experience with Fine-Grain Communication in EM-X Multiprocessor for Parallel Sparse Matrix Computation
Sparse matrix problems require a communication paradigm different from those used in conventional distributed-memory multiprocessors. We present in this paper how fine-grain communication can help obtain high performance in the experimental distributed-memory multiprocessor, EM-X, developed at ETL, which can handle fine-grain communication very efficiently. The sparse matrix kernel, Conjugate G...
متن کامل1.5D Parallel Sparse Matrix-Vector Multiply
There are three common parallel sparse matrix-vector multiply algorithms: 1D row-parallel, 1D column-parallel and 2D row-column-parallel. The 1D parallel algorithms offer the advantage of having only one communication phase. On the other hand, the 2D parallel algorithm is more scalable due to a high level of flexibility on distributing fine-grain tasks, whereas they suffer from two communicatio...
متن کاملUn modèle de programmation à grain fin pour la parallélisation de solveurs linéaires creux. (A fine grain model programming for parallelization of sparse linear solver)
A fine grain model programming for parallelization of sparse linear solver
متن کاملA Matrix Partitioning Interface to PaToH in MATLAB
We present the PaToH MATLAB Matrix Partitioning Interface. The interface provides support for hypergraph-based sparse matrix partitioning methods which are used for efficient parallelization of sparse matrix-vector multiplication operations. The interface also offers tools for visualizing and measuring the quality of a given matrix partition. We propose a novel, multilevel, 2D coarsening-based ...
متن کاملA Nested Dissection Approach to Sparse Matrix Partitioning for Parallel Computations
We consider how to distribute sparse matrices among processes to reduce communication costs in parallel sparse matrix computations, specifically, sparse matrix-vector multiplication. Our main contributions are: (i) an exact graph model for communication with general (two-dimensional) matrix distribution, and (ii) a recursive partitioning algorithm based on nested dissection (substructuring). We...
متن کامل