Approximate algorithms for partitioning problems

Iqbal, Mohammad

doi:10.1007/bf01407812

Cited by 16 publications

(12 citation statements)

References 6 publications

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“…Thus, even if the original partitioning problem has data objects with coordinates in a multidimensional space (typically R 3 ), we restrict our attention to the one-dimensional partitioning problem. This problem is also known as chains-on-chains, and has been well studied [28,40,43]. Again, we are unaware of any results for the multiple load case.…”

Section: Linear Partitioning and Bisectionmentioning

confidence: 99%

LDRD report : parallel repartitioning for optimal solver performance.

Heaphy¹,

Devine²,

Preis

et al. 2004

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We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.

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Section: Linear Partitioning and Bisectionmentioning

confidence: 99%

LDRD report : parallel repartitioning for optimal solver performance.

Heaphy¹,

Devine²,

Preis

et al. 2004

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“…Until recently, the best published algorithm found the optimal partitioning in O(Mmlogm) time, where M is the number of processors and m is the number of modules. This solution and those developed in [11] and [17] all involve repeatedly calling a probe function. A recently discovered dynamic programming formulation [5] reduces the complexity further to O(Mm).…”

Section: LI and Imentioning

confidence: 99%

Rectilinear Partitioning of Irregular Data Parallel Computations

Nicol

1994

Journal of Parallel and Distributed Computing

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This paper describes new mapping algorithms for domain-oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns. We consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network and a relatively slower global network; these partitions heuristically attempt to maximize the fraction of communication carried by the local network. This paper provides an improved algorithm for finding the optimal partition in one dimension, new algorithms for partitioning in two dimensions, and shows that optimal partitioning in three dimensions is NP-complete. We discuss our application of these algorithms to real problems.

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“…The parametric-search approach goes back to Iqbal's work [16] describing an e-approximate algorithm which performs OðlogðW tot =eÞÞ probe calls. Here, W tot denotes the total task weight and e40 denotes the desired accuracy.…”

Section: Introductionmentioning

confidence: 99%

“…Iqbal and Bokhari [17] relaxed the restriction of this algorithm on bounded task weight and communication cost by proposing a condensation algorithm. Iqbal [15] and Nicol [27,29] concurrently proposed an efficient search scheme that finds an optimal partition after only OðP log NÞ probes. Asymptotically more efficient algorithms were proposed by Frederickson [7,8] and Han et al [12].…”

Section: Introductionmentioning

confidence: 99%

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Fast optimal load balancing algorithms for 1D partitioning

Pınar

Aykanat

2004

Journal of Parallel and Distributed Computing

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The one-dimensional decomposition of nonuniform workload arrays with optimal load balancing is investigated. The problem has been studied in the literature as the ''chains-on-chains partitioning'' problem. Despite the rich literature on exact algorithms, heuristics are still used in parallel computing community with the ''hope'' of good decompositions and the ''myth'' of exact algorithms being hard to implement and not runtime efficient. We show that exact algorithms yield significant improvements in load balance over heuristics with negligible overhead. Detailed pseudocodes of the proposed algorithms are provided for reproducibility. We start with a literature review and propose improvements and efficient implementation tips for these algorithms. We also introduce novel algorithms that are asymptotically and runtime efficient. Our experiments on sparse matrix and direct volume rendering datasets verify that balance can be significantly improved by using exact algorithms. The proposed exact algorithms are 100 times faster than a single sparse-matrix vector multiplication for 64-way decompositions on the average. We conclude that exact algorithms with proposed efficient implementations can effectively replace heuristics. r 2004 Elsevier Inc. All rights reserved.

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Approximate algorithms for partitioning problems

Cited by 16 publications

References 6 publications

LDRD report : parallel repartitioning for optimal solver performance.

LDRD report : parallel repartitioning for optimal solver performance.

Rectilinear Partitioning of Irregular Data Parallel Computations

Fast optimal load balancing algorithms for 1D partitioning

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