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Scalability Evaluation of NSLP Algorithm for Solving non-stationary linear programming problems on Cluster Computing Systems 3rd

Scalability Evaluation of NSLP Algorithm for Solving Non-Sta...

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3rd Russian Supercomputing Days (RuSCDays)

作者： Sokolinskaya, Irina Sokolinsky, Leonid B. South Ural State Univ 76 Lenin Prospekt Chelyabinsk 454080 Russia

ISBN: (纸本)9783319712543;9783319712550

The paper is devoted to a scalability study of the NSLP algorithm for solving non-stationary high-dimension linear programming problem on the cluster computing systems. The analysis is based on the BSF model of parallel computations. The BSF model is a new parallel computation model designed on the basis of BSP and SPMD models. The brief descriptions of the NSLP algorithm and the BSF model are given. The NSLP algorithm implementation in the form of a BSF program is considered. On the basis of the BSF cost metric, the upper bound of the NSLP algorithm scalability is derived and its parallel efficiency is estimated. NSLP algorithm implementation using BSF skeleton is described. A comparison of scalability estimations obtained analytically and experimentally is provided.

关键词： non-stationary linear programming problem Large-scale linear programming NSLP algorithm BSF parallel computation model Cost metric Scalability bound Parallel efficiency estimation

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Scalable Algorithm for non-stationary linear programming problems Solving 2

Scalable Algorithm for Non-stationary Linear Programming Pro...

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2nd International Ural Conference on Measurements (UralCon)

作者： Sokolinskaya, I. M. South Ural State Univ Chelyabinsk Russia

ISBN: (纸本)9781538605219

The paper describes a new scalable algorithm called NSLP for high-dimension, non-stationary linear programming problem solving on the modern cluster computing systems. The algorithm consists of two phases: Quest and Targeting. The Quest phase calculates a solution for the system of inequalities defining the constraint system of the linear programming problem under the condition of the input data dynamic changes. To do this, it uses the apparatus of Fejer maps. The Targeting phase forms a special system of points having the shape of the n-dimensional axisymmetric cross. The cross moves in the n-dimensional space in such a way that the solution of the linear programming problem is permanently in the epsilon-vicinity of the cross central point.

关键词： NSLP-algorithm non-stationary linear programming problem large-scale linear programming Fejer map

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Revised Pursuit Algorithm for Solving non-stationary linear programming problems on Modern Computing Clusters with Manycore Accelerators 2nd

Revised Pursuit Algorithm for Solving Non-stationary Linear ...

引用

2nd Russian Supercomputing Days Conference (RuSCDays)

作者： Sokolinskaya, Irina Sokolinsky, Leonid South Ural State Univ 76 Lenin Prospekt Chelyabinsk 454080 Russia

ISBN: (纸本)9783319556680;9783319556697

This paper is devoted to the new edition of the parallel Pursuit algorithm proposed the authors in previous works. The Pursuit algorithm uses Fejer's mappings for building pseudo-projection on polyhedron. The algorithm tracks changes in input data and corrects the calculation process. The previous edition of the algorithm assumed using a cube-shaped pursuit region with the number of K cells in one dimension. The total number of cells is K-n, where n is the problem dimension. This resulted in high computational complexity of the algorithm. The new edition uses a cross-shaped pursuit region with one cross-bar per dimension. Such a region consists of only n(K - 1) + 1 cells. The new algorithm is intended for cluster computing system with Xeon Phi processors.

关键词： non-stationary linear programming problem Fejer's mappings Pursuit algorithm Massive parallelism Cluster computing systems MIC architecture Intel Xeon Phi Native mode OpenMP

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On the Solution of linear programming problems in the Age of Big Data 11th

On the Solution of Linear Programming Problems in the Age of...

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11th International Scientific Conference on Parallel Computational Technologies (PCT)

作者： Sokolinskaya, Irina Sokolinsky, Leonid B. South Ural State Univ 76 Lenin Prospekt Chelyabinsk 454080 Russia

ISBN: (纸本)9783319670355;9783319670348

The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are nonstationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary linear programming problems on modern cluster computing systems. The algorithm consists of two phases: Quest and Targeting. The Quest phase calculates a solution of the system of inequalities defining the constraint system of the linear programming problem under the condition of dynamic changes in input data. To this end, the apparatus of Fejer mappings is used. The Targeting phase forms a special system of points having the shape of an n-dimensional axisymmetric cross. The cross moves in the n-dimensional space in such a way that the solution of the linear programming problem is located all the time in an e-vicinity of the central point of the cross.

关键词： NSLP algorithm non-stationary linear programming problem Large-scale linear programming Fejer mapping

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