Data-Parallel Implementations of Dense Simplex Methods on the Connection Machine CM-2

Eckstein, Jonathan; Boduroğlu, İ. İlkay; Polymenakos, Lazaros; Goldfarb, Donald

doi:10.1287/ijoc.7.4.402

Cited by 20 publications

(19 citation statements)

References 12 publications

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“…Thomadakis & Liu [23] worked on the standard method utilizing the MP-1 and MP-2 MasPar. Eckstein et al [24] showed in the context of the parallel connection machine CM-2 that the iteration time for parallel revised method tended to be higher than for parallel full tableau method even when the revised method is implemented very carefully. Stunkel [25] found a way to parallelize both the revised and standard methods so that both obtained a similar advantage in the context of the parallel Intel iPSC hypercube.…”

Section: Related Workmentioning

confidence: 99%

“…It should also be noted that although dense problems (which suit better the standard method) are uncommon in general, they do occur frequently in some important applications within linear programming [24]. Furthermore, existing distributed memory implementations of the standard simplex method naturally vary in the way that the simplex tableau is distributed among the processors [1,30].…”

Section: Related Workmentioning

confidence: 99%

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Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

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Abstract-The simplex method has been successfully used in solving linear programming (LP) problems for many years. Parallel approaches have also extensively been studied due to the intensive computations required, especially for the solution of large LP problems. Furthermore, the rapid proliferation of multicore CPU architectures as well as the computational power provided by the massive parallelism of modern GPUs have turned CPU / GPU collaboration models increasingly into focus over the last years for better performance. In this paper, a highly scalable implementation framework of the standard full tableau simplex method is first presented, over a hybrid parallel platform which consists of multiple multicore nodes interconnected via a high-speed communication network. The proposed approach is based on the combined use of MPI and OpenMP, adopting a suitable column-based distribution scheme for the simplex tableau. The parallelization framework is then extended in such a way that it can exploit concurrently the full power of the provided resources on a multicore single-node environment with a CUDA-enabled GPU (i.e. using the CPU cores and the GPU concurrently), based on a suitable hybrid multithreading/GPU offloading scheme with OpenMP and CUDA. The corresponding experimental results show that the hybrid MPI+OpenMP based parallelization scheme leads to particularly high speed-up and efficiency values, considerably better than in other competitive approaches, and scaling well even for very large / huge linear problems. Furthermore, the performance of the hybrid multithreading/GPU offloading scheme is clearly superior to both the OpenMP-only and the GPU-only based implementations in almost all cases, which validates the worth of using both resources concurrently. The most important, when it is used in combination with MPI in a multi-node (fully hybrid) environment, it leads to substantial improvements in the speedup achieved for large and very large LP problems.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

View full text Add to dashboard Cite

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“…This is the subject of current research by Boduroglu, Hall and Hogg. Since the approximate steepest edge strategy used by Boduroglu (1997) is based on exact norms of only the entries in the linking rows, these may not be sufficiently good measures to yield the numerical stability and reduction in the number of iterations that was achieved by Boduroglu's dense tableau simplex solver (Eckstein et al 1995). It may be preferable to use Devex (Harris 1973) or, if necessary for numerical stability, accept the significant additional computation and communication overhead of exact steepest edge by implementing the updates described by Goldfarb and Reid (1977).…”

Section: The Standard Simplex Methodsmentioning

confidence: 99%

“…Eckstein et al (1995) parallelised the standard simplex method and the revised simplex method with a dense inverse on the massively parallel Connection Machine CM-2 and CM-5, incorporating the steepest edge pricing strategy directly within their standard simplex implementation, rather than via an update formula for the edge weights as in Goldfarb and Reid (1977). As a consequence of using steepest edge weights and the EXPAND procedure (Gill et al 1989), this implementation is notable for its numerical stability, an issue that has rarely been considered in parallel implementations of the simplex method.…”

Section: Parallel Simplex Using Dense Matrix Algebramentioning

confidence: 99%

“…Given his successful use of steepest edge (Goldfarb and Reid 1977) within his dense standard simplex solver (Eckstein et al 1995), Boduroglu (1997 applied the approximate steepest edge technique of Crowder and Hattingh (1975) in computing weights by using the tableau slice corresponding to linking rows. However, any other edge weight pricing technique for the revised simplex method could be used.…”

Section: Parallelisingmentioning

confidence: 99%

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Towards a practical parallelisation of the simplex method

Hall

2008

Comput Manag Sci

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Peer‐to‐peer distributed text classifier learning in PADMINI

Zhu

Mahule

Dutta

et al. 2012

Statistical Analysis

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Popular Internet document repositories, such as online newspapers, digital libraries, and blogs store large amount of text and image data that are frequently accessed by large number of users. Users' input through collaborative commenting or tagging can be very useful in organizing and classifying documents. Some web sites (e.g. Google Image Labeler) support a collection of tags and labels, but a large fraction of these sites do not currently support such activities. Moreover, relying upon centrally controlled web‐service providers for such support is probably not a good idea if the objective is to make the collaborative inputs publicly available. Often, business entities offering such web‐based tagging environments end up owning and monetizing the result of the collective effort. This paper takes a step toward addressing this problem—it proposes a peer‐to‐peer (P2P) system (PADMINI), powered by distributed data mining algorithms. In particular, it focuses on learning a P2P classifier from tagged text data. This paper describes the PADMINI system and the distributed text classifier learning components; text classification is posed as a linear program and an asynchronous distributed algorithm is used to solve it. It also presents extensive empirical results on text data obtained from the Hubble Space Telescope (HST) proposal abstract database. Copyright © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 2012

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Data-Parallel Implementations of Dense Simplex Methods on the Connection Machine CM-2

Cited by 20 publications

References 12 publications

Simplex Parallelization in a Fully Hybrid Hardware Platform

Simplex Parallelization in a Fully Hybrid Hardware Platform

Towards a practical parallelisation of the simplex method

Peer‐to‐peer distributed text classifier learning in PADMINI

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