Developing Subdomain Allocation Algorithms Based on Spatial and Communicational Constraints to Accelerate Dust Storm Simulation

Dust storm has serious disastrous impacts on environment, human health, and assets. The developments and applications of dust storm models have contributed significantly to better understand and predict the distribution, intensity and structure of dust storms. However, dust storm simulation is a data and computing intensive process. To improve the computing performance, high performance computing has been widely adopted by dividing the entire study area into multiple subdomains and allocating each subdomain on different computing nodes in a parallel fashion. Inappropriate allocation may introduce imbalanced task loads and unnecessary communications among computing nodes. Therefore, allocation is a key factor that may impact the efficiency of parallel process. An allocation algorithm is expected to consider the computing cost and communication cost for each computing node to minimize total execution time and reduce overall communication cost for the entire simulation. This research introduces three algorithms to optimize the allocation by considering the spatial and communicational constraints: 1) an Integer Linear Programming (ILP) based algorithm from combinational optimization perspective; 2) a K-Means and Kernighan-Lin combined heuristic algorithm (K&K) integrating geometric and coordinate-free methods by merging local and global partitioning; 3) an automatic seeded region growing based geometric and local partitioning algorithm (ASRG). The performance and effectiveness of the three algorithms are compared based on different factors. Further, we adopt the K&K algorithm as the demonstrated algorithm for the experiment of dust model simulation with the non-hydrostatic mesoscale model (NMM-dust) and compared the performance with the MPI default sequential allocation. The results demonstrate that K&K method significantly improves the simulation performance with better subdomain allocation. This method can also be adopted for other relevant atmospheric and numerical modeling.

[1]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

[2]  David Portugal,et al.  A Survey on Multi-robot Patrolling Algorithms , 2011, DoCEIS.

[3]  J. Ramanujam,et al.  Cluster partitioning approaches to mapping parallel programs onto a hypercube , 1987, Parallel Comput..

[4]  Frank Y. Shih,et al.  Automatic seeded region growing for color image segmentation , 2005, Image Vis. Comput..

[5]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  R. M. Mattheyses,et al.  A Linear-Time Heuristic for Improving Network Partitions , 1982, 19th Design Automation Conference.

[7]  Ann B. Lee,et al.  Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Frank Thomson Leighton,et al.  Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms , 1999, JACM.

[9]  Qunying Huang,et al.  Using spatial principles to optimize distributed computing for enabling the physical science discoveries , 2011, Proceedings of the National Academy of Sciences.

[10]  Christina Freytag,et al.  Using Mpi Portable Parallel Programming With The Message Passing Interface , 2016 .

[11]  Klaudia Frankfurter Computers And Intractability A Guide To The Theory Of Np Completeness , 2016 .

[12]  Vipin Kumar,et al.  Graph partitioning for high-performance scientific simulations , 2003 .

[13]  Shashi Shekhar,et al.  Multilevel hypergraph partitioning: applications in VLSI domain , 1999, IEEE Trans. Very Large Scale Integr. Syst..

[14]  Byung Ro Moon,et al.  Genetic Algorithm and Graph Partitioning , 1996, IEEE Trans. Computers.

[15]  Joseph Naor,et al.  Fast approximate graph partitioning algorithms , 1997, SODA '97.

[16]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[17]  John R. Gilbert,et al.  A parallel graph partitioning algorithm for a message-passing multiprocessor , 1987, International journal of parallel programming.

[18]  David E. van den Bout,et al.  Graph partitioning using annealed neural networks , 1990, International 1989 Joint Conference on Neural Networks.

[19]  John R. Gilbert,et al.  A parallel graph partitioning algorithm for a message-passing multiprocessor , 1987, International Journal of Parallel Programming.

[20]  Robert van Engelen,et al.  Graph Partitioning for High Performance Scienti c Simulations , 2000 .

[21]  Suresh Chalasani,et al.  Equivalence between SP2 high-performance switches and three-stage Clos networks , 1996, Proceedings of the 1996 ICPP Workshop on Challenges for Parallel Processing.

[22]  James V. Hansen,et al.  Task allocation in distributed processing systems , 1986 .

[23]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[24]  Franz Rendl,et al.  Graph partitioning using linear and semidefinite programming , 2003, Math. Program..

[25]  G. Kallos,et al.  A model for prediction of desert dust cycle in the atmosphere , 2001 .

[26]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[27]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[28]  Shahid H. Bokhari,et al.  A Partitioning Strategy for Nonuniform Problems on Multiprocessors , 1987, IEEE Transactions on Computers.

[29]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[30]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[31]  Scott F. Midkiff,et al.  Heuristic Technique for Processor and Link Assignment in Multicomputers , 1991, IEEE Trans. Computers.

[32]  Julio Ortega Lopera,et al.  A Parallel Multilevel Metaheuristic for Graph Partitioning , 2004, J. Heuristics.

[33]  Bora Uçar,et al.  Task assignment in heterogeneous computing systems , 2006, J. Parallel Distributed Comput..

[34]  Dayong Ye,et al.  A Dynamic Coordination Approach for Task Allocation in Disaster Environments under Spatial and Communicational Constraints , 2014 .

[35]  Thomas Stützle,et al.  The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances , 2003 .

[36]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[37]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[38]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[39]  Vipin Kumar,et al.  Parallel Multilevel series k-Way Partitioning Scheme for Irregular Graphs , 1999, SIAM Rev..

[40]  Eric E. Aubanel,et al.  PaGrid: A Mesh Partitioner for Computational Grids , 2006, Journal of Grid Computing.

[41]  A. Abdel-azim Fundamentals of Heat and Mass Transfer , 2011 .

[42]  Steven Warren Hammond,et al.  Mapping unstructured grid computations to massively parallel computers , 1992 .

[43]  Gary L. Miller,et al.  Automatic Mesh Partitioning , 1992 .

[44]  Geoffrey C. Fox,et al.  Fast and parallel mapping algorithms for irregular problems , 1996, The Journal of Supercomputing.

[45]  Mark Jerrum,et al.  Simulated annealing for graph bisection , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[46]  Bin Zhou,et al.  High-performance computing for the simulation of dust storms , 2010, Comput. Environ. Urban Syst..

[47]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[48]  Mandhapati P. Raju,et al.  Domain Decomposition Based High Performance Parallel Computing , 2009, ArXiv.

[49]  Inderjit S. Dhillon,et al.  Kernel k-means: spectral clustering and normalized cuts , 2004, KDD.

[50]  B. Nour-Omid,et al.  Solving finite element equations on concurrent computers , 1987 .

[51]  Clive F. Baillie,et al.  Regional Weather Modeling on Parallel Computers , 1997, Parallel Comput..

[52]  Frank P. Incropera,et al.  Fundamentals of Heat and Mass Transfer , 1981 .

[53]  Rupak Biswas,et al.  A new procedure for dynamic adaption of three-dimensional unstructured grids , 1993 .

[54]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[55]  Julio Ortega,et al.  Multilevel Heuristic Algorithm for Graph Partitioning , 2003, EvoWorkshops.

[56]  Thang Nguyen Bui,et al.  An Ant System Algorithm For Graph Bisection , 2002, GECCO.

[57]  Scott F. Midkiff,et al.  Processor and Link Assignment in Multicomputers Using Simulated Annealing , 1988, ICPP.

[58]  Norman E. Gibbs,et al.  A Comparison of Several Bandwidth and Profile Reduction Algorithms , 1976, TOMS.

[59]  Chris H. Q. Ding,et al.  Bipartite graph partitioning and data clustering , 2001, CIKM '01.

[60]  室 章治郎 Michael R.Garey/David S.Johnson 著, "COMPUTERS AND INTRACTABILITY A guide to the Theory of NP-Completeness", FREEMAN, A5判変形判, 338+xii, \5,217, 1979 , 1980 .

[61]  Qunying Huang,et al.  Using adaptively coupled models and high-performance computing for enabling the computability of dust storm forecasting , 2013, Int. J. Geogr. Inf. Sci..

[62]  Gary L. Miller,et al.  Geometric mesh partitioning: implementation and experiments , 1995, Proceedings of 9th International Parallel Processing Symposium.

[63]  Sunling Gong,et al.  CUACE/Dust – an integrated system of observation and modeling systems for operational dust forecasting in Asia , 2007 .

[64]  Satish Rao,et al.  Graph partitioning using single commodity flows , 2006, STOC '06.

[65]  J. Mandel Balancing domain decomposition , 1993 .

[66]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[67]  Brian W. Kernighan,et al.  A Procedure for Placement of Standard-Cell VLSI Circuits , 1985, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[68]  Peter Koroÿsec,et al.  A MULTILEVEL ANT-COLONY OPTIMIZATION ALGORITHM FOR MESH PARTITIONING , 2003 .

[69]  Shahid H. Bokhari,et al.  On the Mapping Problem , 1981, IEEE Transactions on Computers.

[70]  H. M. Wagner Linear Programming Techniques for Regression Analysis , 1959 .

[71]  G. Madey,et al.  Examining the impact of larval source management and insecticide-treated nets using a spatial agent-based model of Anopheles gambiae and a landscape generator tool , 2013, Malaria Journal.

[72]  Martin G. Everett,et al.  Partitioning & Mapping of Unstructured Meshes to Parallel Machine Topologies , 1995, IRREGULAR.

[73]  Juan Shan,et al.  A completely automatic segmentation method for breast ultrasound images using region growing , 2008 .

[74]  Prithviraj Banerjee Parallel algorithms for VLSI computer-aided design , 1994 .

[75]  David S. Johnson,et al.  Some simplified NP-complete problems , 1974, STOC '74.

[76]  Pei-Yung Hsiao,et al.  A Fuzzy Clustering Algorithm for Graph Bisection , 1994, Inf. Process. Lett..

[77]  Andrew B. Kahng,et al.  Recent directions in netlist partitioning: a survey , 1995, Integr..

[78]  Francine Berman,et al.  On Mapping Parallel Algorithms into Parallel Architectures , 1987, J. Parallel Distributed Comput..