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Scalability
Published in Vivek Kale, Digital Transformation of Enterprise Architecture, 2019
It is obvious that for a totally parallelizable program (σ = 0), the speed up is p. However, since in practice, σ < 1, the speedup is sublinear and is in fact bounded by a constant, which it approaches depending upon an asymptotically increasing number of processors. Effectively, a very high percentage of parallelizable code is imperative for a program to be truly fast: even programs that have 99% parallelizable code running on 100 nodes are only sped up by a factor of 50! Just as the speed of light defines the theoretical limit of how fast we can travel in our universe, Amdahl’s law defines the limits of performance gain we can achieve by adding more nodes to clusters.
Supercomputing in the 1990s A Distributed Solution
Published in Hojjat Adeli, Supercomputing in Engineering Analysis, 2020
S. Ashley Burns, Charlie F. Bender
Goeffrey Fox from the California Institute of Technology has cowritten a volume describing parallel implementations of common scientific constructs in great detail (Fox et al., 1988). Among the applications he identifies as effectively parallelizable using the methods presented are structural analysis, computational fluid dynamics (Navier-Stokes and Euler applications), plasma physics, image processing, electronic structure, protein mechanics, seismic modeling, turbulence, high-energy physics data analysis, and many more. Implementation techniques such as those presented, if widely publicized, can further the education of engineers and ease acceptance of parallel systems.
A heuristic scheme for multivariate set partitioning problems with application to classifying heterogeneous populations for multiple binary attributes
Published in IISE Transactions, 2022
Hadi El-Amine, Hrayer Aprahamian
In this article, we provide an efficient heuristic to solve a class of multivariate set partitioning problems in which each item is characterized by three attributes. Our analytical results enable us to identify a sequence of orderings of the items that lead to good-performing solutions. This, in turn, enables us to construct a heuristic algorithm in which a sequence of shortest path problems are solved. The proposed algorithm runs in polynomial-time and is independent of the number of groups in the partition. Moreover the proposed algorithm is parallelizable, which can be taken advantage of in order to reduce computational time. Some of the characteristics shown in this article continue to hold in the higher-dimensional case, and hence, our approach also sheds light on the multivariate case in which each item is characterized by a vector of attributes.
Meta-Kriging: Scalable Bayesian Modeling and Inference for Massive Spatial Datasets
Published in Technometrics, 2018
Rajarshi Guhaniyogi, Sudipto Banerjee
This article has developed a practical approximation to Bayesian spatial inference for “big-N” problems. We propose dividing big datasets into multiple subsets, carrying out independent inference in each subset followed by combining inference from all subsets. The entire procedure is “trivially parallelizable,” offers rapid computation for big data and also eliminates the need to store the entire dataset in one processor. The approach seems to accrue dramatic gains in computation and storage and offers inference essentially indistinguishable from full Gaussian process models and other competitive approaches for big spatial data. Further, SMK provides a generic “divide and conquer” algorithm that is potentially applicable to any spatial process model for data subsets. For example, SMK can be applied to scalable Gaussian process models, such as predictive processes and nearest-neighbor Gaussian processes, to considerably enhance gains in computation and storage.