Linear algebra algorithms in a heterogeneous cluster of personal computers

Barbosa, Jorge G.; Tavares, João Manuel R. S.; Padilha, Armando Jorge Monteiro Neves

doi:10.1109/hcw.2000.843740

Cited by 28 publications

(17 citation statements)

References 15 publications

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“…Matrix multiplication has been studied by [25], [2]. LU and QR decomposition have been discussed by Barbosa et al [1]. Static partitioning schemes to map a two-dimensional data matrix onto heterogeneous resources have been investigated by Crandall and Quinn [14], Kaddoura et al [24], and Beaumont et al [3].…”

Section: Resultsmentioning

confidence: 99%

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Mapping and load-balancing iterative computations

Legrand

Renard

Robert

et al. 2004

IEEE Trans. Parallel Distrib. Syst.

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Abstract-This paper is devoted to mapping iterative algorithms onto heterogeneous clusters. The application data is partitioned over the processors, which are arranged along a virtual ring. At each iteration, independent calculations are carried out in parallel, and some communications take place between consecutive processors in the ring. The question is to determine how to slice the application data into chunks, and to assign these chunks to the processors, so that the total execution time is minimized. One major difficulty is to embed a processor ring into a network that typically is not fully connected, so that some communication links have to be shared by several processor pairs. We establish a complexity result that assesses the difficulty of this problem, and we design a practical heuristic that provides efficient mapping, routing, link-sharing, and data distribution schemes.

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Section: Resultsmentioning

confidence: 99%

“…. In the summation P r s¼1 c ðsÞ;ðsÀ1Þ þc ðsÞ;ðsþ1Þ w ðsÞ , we suppress the two terms corresponding to the two paths between P i to P j (by hypothesis we had i ¼ ðsÞ 1. We did not express in (4) the inequations stating that all the unknowns are nonnegative.…”

Section: Ring Constructionmentioning

confidence: 99%

Mapping and load-balancing iterative computations

Legrand

Renard

Robert

et al. 2004

IEEE Trans. Parallel Distrib. Syst.

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“…It ranges from data partitioning for parallel video processing [2] to finding the optimal number of processors in linear algebra algorithms [4]. More generally, many results have been produced by the divisible load theory for various network topologies (see [10] for an overview).…”

Section: Related Workmentioning

confidence: 99%

Load-balancing scatter operations for grid computing

2004

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We present solutions to statically load-balance scatter operations in parallel codes run on grids. Our load-balancing strategy is based on the modification of the data distributions used in scatter operations. We study the replacement of scatter operations with parameterized scatters, allowing custom distributions of data. The paper presents: (1) a general algorithm which finds an optimal distribution of data across processors; (2) a quicker guaranteed heuristic relying on hypotheses on communications and computations; (3) a policy on the ordering of the processors. Experimental results with an MPI scientific code illustrate the benefits obtained from our load-balancing.

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“…Several authors [17,32,31,40,21] propose a mapping policy which dynamically minimizes system degradation (including the cost of remapping) for each computation step. Static strategies aiming at distributing independent chunks of work to two-dimensional processor grids are studied in [1,2]. Relaxing the geometrical constraints induced by two-dimensional grids leads to irregular partitionings [12,22,3] that allow for a good loadbalancing but are much more difficult to implement.…”

Section: Related Workmentioning

confidence: 99%

Data Redistribution Algorithms for Heterogeneous Processor Rings

Renard¹,

Robert

Vivien

2006

The International Journal of High Performance Computing Applica

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We consider the problem of redistributing data on homogeneous and heterogeneous ring of processors. The problem arises in several applications, each time after that a load-balancing mechanism is invoked (but we do not discuss the load-balancing mechanism itself). We provide algorithms that aim at optimizing the data redistribution, both for uni-directional and bi-directional rings, and we give complete proofs of correctness. One major contribution of the paper is that we are able to prove the optimality of the proposed algorithms in all cases except that of a bi-directional heterogeneous ring, for which the problem remains open. Keywords: Heterogeneous rings, data redistribution algorithms, load-balancing RésuméDans ce rapport, nous nous intéressons au problème de redistribution de données sur des anneaux de processeurs homogènes et hétérogènes. Ce problème surgit dans plusieurs applications, après chaque phase d'équilibrage de charge (nous ne discutons pas ici du mécanisme d'équilibrage de charge lui-même). Nous proposons des algorithmes qui visentà optimiser la redistribution de données pour des anneaux unidirectionnels et bidirectionnels, et nous donnons toutes les preuves de correction de ces algorithmes. Une des contributions principales de ce rapport est que nous pouvons prouver l'optimialité des algorithmes proposés dans tous les cas, sauf dans le cas d'un anneau hétérogène bidirectionnel, pour lequel le problème reste ouvert.

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Linear algebra algorithms in a heterogeneous cluster of personal computers

Abstract: Cluster computing is presently a major research area, mostly for high performance computing.

Cited by 28 publications

References 15 publications

Mapping and load-balancing iterative computations

Mapping and load-balancing iterative computations

Load-balancing scatter operations for grid computing

Data Redistribution Algorithms for Heterogeneous Processor Rings

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