Fast optimal load balancing algorithms for 1D partitioning

Pınar, Ali; Aykanat, Cevdet

doi:10.1016/j.jpdc.2004.05.003

Cited by 91 publications

(82 citation statements)

References 27 publications

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“…Jagged-like partitioning method. Jagged partitioning has been successively used in partitioning 2D spatial computational domains (2D workload arrays) for load balancing in the parallelization of several irregular computations including SpMxV computations on processor meshes [31,38,40,41,42]. In this method, for a P × Q processor mesh, the matrix is first partitioned into P horizontal (vertical) strips and every horizontal (vertical) strip is independently partitioned into Q submatrices.…”

Section: Hypergraph Models For 1d Sparse Matrix Partitioningmentioning

confidence: 99%

On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe

Çatalyürek¹,

Aykanat²,

Uçar³

2010

SIAM J. Sci. Comput.

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Abstract. We consider two-dimensional partitioning of general sparse matrices for parallel sparse matrix-vector multiply operation. We present three hypergraph-partitioning-based methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces fine-grain partitions. The other two produce coarser partitions, where one of them imposes a limit on the number of messages sent and received by a single processor, and the other trades that limit for a lower communication volume. We also present a thorough experimental evaluation of the proposed two-dimensional partitioning methods together with the hypergraph-based one-dimensional partitioning methods, using an extensive set of public domain matrices. Furthermore, for the users of these partitioning methods, we present a partitioning recipe that chooses one of the partitioning methods according to some matrix characteristics.Key words. sparse matrix partitioning, parallel matrix-vector multiplication, hypergraph partitioning, two-dimensional partitioning, combinatorial scientific computing AMS subject classifications. 05C50, 05C65, 65F10, 65F50, 65Y05 DOI. 10.1137/080737770 1. Introduction. Sparse matrix-vector multiply operation forms the computational core of many iterative methods including solvers for linear systems, linear programs, eigensystems, and least squares problems. In these solvers, the computations y ← Ax are performed repeatedly with the same large, sparse, possibly unsymmetric or rectangular matrix A and with a changing input vector x. Our aim is to efficiently parallelize these multiply operations by two-dimensional (2D) partitioning of the matrix A in such a way that the computational load per processor is balanced and the communication overhead is low.Graph and hypergraph partitioning models have been used for one-dimensional (1D) partitioning of sparse matrices [4,5,8,9,19,20,25,26,30,32,37]. In these models, a K-way partition of the vertices of a given graph or hypergraph is computed. The partitioning constraint is to maintain a balance criterion on the number of vertices in each part; if the vertices are weighted, then the constraint is to maintain a balance criterion on the sum of the vertex weights in each part. The partitioning objective is to minimize the cutsize of the partition defined over the edges or hyperedges. The partitioning constraint and objective relate, respectively to, maintaining a computational

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Section: Hypergraph Models For 1d Sparse Matrix Partitioningmentioning

confidence: 99%

On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe

Çatalyürek¹,

Aykanat²,

Uçar³

2010

SIAM J. Sci. Comput.

Self Cite

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“…Our interval based approach for load balancing among PEs could be modeled as a chain-on-chain problem (CCP) [8]. The CCP problem has been widely studied, and various efficient polynomial time algorithms have been proposed [9], [10], [11].…”

Section: Related Workmentioning

confidence: 99%

Customized MPSoC synthesis for task sequence

Chen

Boichat

Mitra

2011

2011 IEEE 9th Symposium on Application Specific Processors (SASP)

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Abstract-Multiprocessor System-on-Chip (MPSoC) platforms have become increasingly popular for high-performance embedded applications. Each processing element (PE) on such platforms can be tuned to match the computational demands of the tasks executing on it, creating a heterogeneous multiprocessor system. Extensible processor cores, where the base instruction-set architecture can be augmented with application-specific custom instructions, have recently emerged as flexible building blocks for heterogeneous MPSoC platforms. However, the customization of the different PEs has to be carried out in a synergistic manner so as to create an optimal system. In this work, we propose a pseudopolynomial time algorithm to design the most resource-efficient customized MPSoC platform for mapping linear task graphs representing streaming applications, under deadline constraints. Experimental validation with MP3 encoder and MPEG-2 encoder applications confirms the efficiency of our approach.

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“…We have also discussed the relationship with the chains-to-chains problem [10,14,16,17,22,23] in Sect. 1.…”

Section: Related Workmentioning

confidence: 99%

“…, a n , this problem is to partition the array into p intervals whose element sums are well balanced (technically, the aim is to minimize the largest sum of the elements of any interval). This problem has been extensively studied in the literature (see the pioneering papers [10,14,22] and the survey [23]). It amounts to load-balance n computations whose ordering must be preserved (hence the restriction to intervals) onto p identical processors.…”

Section: Introductionmentioning

confidence: 99%

Complexity Results for Throughput and Latency Optimization of Replicated and Data-parallel Workflows

Benoît

Robert

2008

Algorithmica

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Mapping applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline or fork graphs. Several antagonist criteria should be optimized for workflow applications, such as throughput and latency (or a combination). In this paper, we consider a simplified model with no communication cost, and we provide an exhaustive list of complexity results for different problem instances. Pipeline or fork stages can be replicated in order to increase the throughput by sending consecutive data sets onto different processors. In some cases, stages can also be data-parallelized, i.e. the computation of one single data set is shared between several processors. This leads to a decrease of the latency and an increase of the throughput. Some instances of this simple model are shown to be NP-hard, thereby exposing the inherent complexity of the mapping problem. We provide polynomial algorithms for other problem instances. Altogether, we provide solid theoretical foundations for the study of mono-criterion or bi-criteria mapping optimization problems.

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Fast optimal load balancing algorithms for 1D partitioning

Cited by 91 publications

References 27 publications

On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe

On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe

Customized MPSoC synthesis for task sequence

Complexity Results for Throughput and Latency Optimization of Replicated and Data-parallel Workflows

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