Sparse matrix-vector multiplication (shortly spMV) and transposed spMV (shortly spMTV) are the most common routines in the numerical linear algebra. Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Since the commonly used storage formats (like COO or CSR) are not sufficient for high-performance computations, extensive research has been conducted about maximal computational efficiency of these routines. For modern CPU architectures, the main bottleneck of these routines is the limited memory bandwidth. In this paper, we introduce a new approach for these routines for modern processor architectures using a space efficient hierarchical format, which can significantly reduce the amount of transferred data from memory for almost all types of matrices arising from various application disciplines. This format represents a trade-off between space and execution efficiency. The performance of these routines with this format seems to be very close to the hardware limits.
{"title":"Space and Execution Efficient Formats for Modern Processor Architectures","authors":"I. Šimeček, D. Langr","doi":"10.1109/SYNASC.2015.24","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.24","url":null,"abstract":"Sparse matrix-vector multiplication (shortly spMV) and transposed spMV (shortly spMTV) are the most common routines in the numerical linear algebra. Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Since the commonly used storage formats (like COO or CSR) are not sufficient for high-performance computations, extensive research has been conducted about maximal computational efficiency of these routines. For modern CPU architectures, the main bottleneck of these routines is the limited memory bandwidth. In this paper, we introduce a new approach for these routines for modern processor architectures using a space efficient hierarchical format, which can significantly reduce the amount of transferred data from memory for almost all types of matrices arising from various application disciplines. This format represents a trade-off between space and execution efficiency. The performance of these routines with this format seems to be very close to the hardware limits.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"677 1","pages":"98-105"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74750121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Our goal is to present a basic, novel, and correct SAT solver algorithm, show its soundness, compare it with a standard SAT solver, give some ideas in which cases might it be competitive. We do not present a fine-tuned, state-of-the-art SAT solver, only a new basic algorithm. So we introduce CCC, a SAT solver algorithm which is an iterative version of the inclusion-exclusion principle. CCC stands for Counting Clear Clauses. It counts those full length (in our terminology: clear) clauses, which are subsumed by the input SAT problem. Full length clauses are n-clauses, where n is the number of variables in the input problem. A SAT problem is satisfiable if it does not subsume all n-clauses. The idea is that in an n-clause each of n variables is present either as a positive literal or as a negative one. So we can represent them by n bits. CCC is motivated by the inclusion-exclusion principle, it counts full length clauses as the principle does in case of the SAT problem, but in an iterative way. It works in the following way: It sets its counter to be 0. It converts 0 to an n-clause, which is the one with only negative literals. It checks whether this n-clause is subsumed by the input SAT problem. If yes, it increases the counter and repeats the loop. If not, we have a model, which is given by the negation of this n-clause. We show that almost always we can increase the counter by more than one. We show that this algorithm always stops and finds a model if there is one. We present a worst case time complexity analysis and lot of test results. The test results show that this basic algorithm can outperform a standard SAT solver, although its implementation is very simple without any optimization. CCC is competitive if the input problem contains lot of short clauses. Our implementation can be downloaded and the reader is welcome to make a better solver out of it. We believe that this new algorithm could serve as a good basis for parallel algorithms, because its memory usage is constant and no communication is needed between the nodes.
{"title":"Solving SAT by an Iterative Version of the Inclusion-Exclusion Principle","authors":"Gábor Kusper, C. Biró","doi":"10.1109/SYNASC.2015.38","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.38","url":null,"abstract":"Our goal is to present a basic, novel, and correct SAT solver algorithm, show its soundness, compare it with a standard SAT solver, give some ideas in which cases might it be competitive. We do not present a fine-tuned, state-of-the-art SAT solver, only a new basic algorithm. So we introduce CCC, a SAT solver algorithm which is an iterative version of the inclusion-exclusion principle. CCC stands for Counting Clear Clauses. It counts those full length (in our terminology: clear) clauses, which are subsumed by the input SAT problem. Full length clauses are n-clauses, where n is the number of variables in the input problem. A SAT problem is satisfiable if it does not subsume all n-clauses. The idea is that in an n-clause each of n variables is present either as a positive literal or as a negative one. So we can represent them by n bits. CCC is motivated by the inclusion-exclusion principle, it counts full length clauses as the principle does in case of the SAT problem, but in an iterative way. It works in the following way: It sets its counter to be 0. It converts 0 to an n-clause, which is the one with only negative literals. It checks whether this n-clause is subsumed by the input SAT problem. If yes, it increases the counter and repeats the loop. If not, we have a model, which is given by the negation of this n-clause. We show that almost always we can increase the counter by more than one. We show that this algorithm always stops and finds a model if there is one. We present a worst case time complexity analysis and lot of test results. The test results show that this basic algorithm can outperform a standard SAT solver, although its implementation is very simple without any optimization. CCC is competitive if the input problem contains lot of short clauses. Our implementation can be downloaded and the reader is welcome to make a better solver out of it. We believe that this new algorithm could serve as a good basis for parallel algorithms, because its memory usage is constant and no communication is needed between the nodes.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"284 1","pages":"189-190"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75858647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A combinatorial condition called well distributedoccurrences, or WELLDOC for short, has been introducedrecently. The proofs that WELLDOC property holds for thefamily of Sturmian words, and more generally, for Arnoux-Rauzy words are given in two papers by Balkova et al. The WELLDOC property for bounded bi-ideals is analysed inthis paper. The existence of a 1-bounded bi-ideal over thefinite alphabet that satisfies the WELLDOC property has beenproved by the authors.
{"title":"On the Existence of 1-Bounded Bi-ideals with the WELLDOC Property","authors":"Raivis Bēts, J. Buls","doi":"10.1109/SYNASC.2015.57","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.57","url":null,"abstract":"A combinatorial condition called well distributedoccurrences, or WELLDOC for short, has been introducedrecently. The proofs that WELLDOC property holds for thefamily of Sturmian words, and more generally, for Arnoux-Rauzy words are given in two papers by Balkova et al. The WELLDOC property for bounded bi-ideals is analysed inthis paper. The existence of a 1-bounded bi-ideal over thefinite alphabet that satisfies the WELLDOC property has beenproved by the authors.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"33 1","pages":"320-324"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77303098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As a general rule, each user must provide thetool applied with particular values of its input parameters. Aninexperienced user may hardly figure out their values and thetool developer must define the default values in order to helpher/him. We present an approach to solve the problem with thehelp of multi-criteria optimization that is new in this formulation. We demonstrate our approach in closer details using an examplefrom the automatic definition of optimal default parameters forreal-time merging of visual objects. Our approach is generic andmay be also used for any kind of such inverse problems.
{"title":"Automatic Definition of Optimal Default Parameters of Models: Image Matting Application","authors":"E. Ravve, Z. Volkovich, G. Weber","doi":"10.1109/SYNASC.2015.47","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.47","url":null,"abstract":"As a general rule, each user must provide thetool applied with particular values of its input parameters. Aninexperienced user may hardly figure out their values and thetool developer must define the default values in order to helpher/him. We present an approach to solve the problem with thehelp of multi-criteria optimization that is new in this formulation. We demonstrate our approach in closer details using an examplefrom the automatic definition of optimal default parameters forreal-time merging of visual objects. Our approach is generic andmay be also used for any kind of such inverse problems.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"12 1","pages":"251-254"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88416280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Parallel code design is a challenging task especially when addressing petascale systems for massive parallel processing (MPP), i.e. parallel computations on several hundreds of thousands of cores. An in-house computational fluid dynamics code, developed by our group, was designed for such high-fidelity runs in order to exhibit excellent scalability values. Basis for this code is an adaptive hierarchical data structure together with an efficient communication and (numerical) computation scheme that supports MPP. For a detailled scalability analysis, we performed several experiments on two of Germany's national supercomputers up to 140,000 processes. In this paper, we will show the results of those experiments and discuss any bottlenecks that could be observed while solving engineering-based problems such as porous media flows or thermal comfort assessments for problem sizes up to several hundred billion degrees of freedom.
{"title":"Measuring and Comparing the Scaling Behaviour of a High-Performance CFD Code on Different Supercomputing Infrastructures","authors":"J. Frisch, R. Mundani","doi":"10.1109/SYNASC.2015.63","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.63","url":null,"abstract":"Parallel code design is a challenging task especially when addressing petascale systems for massive parallel processing (MPP), i.e. parallel computations on several hundreds of thousands of cores. An in-house computational fluid dynamics code, developed by our group, was designed for such high-fidelity runs in order to exhibit excellent scalability values. Basis for this code is an adaptive hierarchical data structure together with an efficient communication and (numerical) computation scheme that supports MPP. For a detailled scalability analysis, we performed several experiments on two of Germany's national supercomputers up to 140,000 processes. In this paper, we will show the results of those experiments and discuss any bottlenecks that could be observed while solving engineering-based problems such as porous media flows or thermal comfort assessments for problem sizes up to several hundred billion degrees of freedom.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"34 1","pages":"371-378"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74373392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that Lagrange inversion can be used to obtain closed-form expressions for a number of series expansions of the Lambert W function. Equivalently, we obtain expressions for the nth derivative. Various integer sequences related to the series expansions now can be expressed in closed form.
{"title":"Lagrange Inversion and Lambert W","authors":"D. J. Jeffrey, G. Kalugin, N. Murdoch","doi":"10.1109/SYNASC.2015.16","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.16","url":null,"abstract":"We show that Lagrange inversion can be used to obtain closed-form expressions for a number of series expansions of the Lambert W function. Equivalently, we obtain expressions for the nth derivative. Various integer sequences related to the series expansions now can be expressed in closed form.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"59 1","pages":"42-46"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84504589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexandru-Ciprian Zavoianu, E. Lughofer, G. Bramerdorfer, W. Amrhein, Susanne Saminger-Platz
By employing state-of-the-art automated design and optimization techniques from the field of evolutionary computation, engineers are able to discover electrical machine designs that are highly competitive with respect to several objectives like efficiency, material costs, torque ripple and others. Apart from being Pareto-optimal, a good electrical machine design must also be quite robust, i.e., it must not be sensitive with regard to its design parameters as this would severely increase manufacturing costs or make the physical machine exhibit characteristics that are very different from those of its computer simulation model. Even when using a modern parallel/distributed computing environment, carrying out a (global) tolerance analysis of an electrical machine design is extremely challenging because of the number of evaluations that must be performed and because each evaluation requires very time-intensive non-linear finite element (FE) simulations. In the present research, we describe how global surrogate models (ensembles of fast-to-train artificial neural networks) that are created in order to speed-up the multi-objective evolutionary search can be easily reused to perform a fast tolerance analysis of the optimized designs. Using two industrial optimization scenarios, we show that the surrogate-based approach can offer very valuable insights regarding the local and global sensitivities of the considered objectives at a fraction of the computational cost required by a FE-based strategy. Encouraged by the good performance on individual designs, we also used the surrogate approach to track the average sensitivity of the Pareto front during the entire optimization procedure. Our results indicate that there is no generalized increase of sensitivity during the runs, i.e., the used evolutionary algorithms do not enter a stage where they discover electrical drive designs that trade robustness for quality.
{"title":"A Surrogate-Based Strategy for Multi-objective Tolerance Analysis in Electrical Machine Design","authors":"Alexandru-Ciprian Zavoianu, E. Lughofer, G. Bramerdorfer, W. Amrhein, Susanne Saminger-Platz","doi":"10.1109/SYNASC.2015.39","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.39","url":null,"abstract":"By employing state-of-the-art automated design and optimization techniques from the field of evolutionary computation, engineers are able to discover electrical machine designs that are highly competitive with respect to several objectives like efficiency, material costs, torque ripple and others. Apart from being Pareto-optimal, a good electrical machine design must also be quite robust, i.e., it must not be sensitive with regard to its design parameters as this would severely increase manufacturing costs or make the physical machine exhibit characteristics that are very different from those of its computer simulation model. Even when using a modern parallel/distributed computing environment, carrying out a (global) tolerance analysis of an electrical machine design is extremely challenging because of the number of evaluations that must be performed and because each evaluation requires very time-intensive non-linear finite element (FE) simulations. In the present research, we describe how global surrogate models (ensembles of fast-to-train artificial neural networks) that are created in order to speed-up the multi-objective evolutionary search can be easily reused to perform a fast tolerance analysis of the optimized designs. Using two industrial optimization scenarios, we show that the surrogate-based approach can offer very valuable insights regarding the local and global sensitivities of the considered objectives at a fraction of the computational cost required by a FE-based strategy. Encouraged by the good performance on individual designs, we also used the surrogate approach to track the average sensitivity of the Pareto front during the entire optimization procedure. Our results indicate that there is no generalized increase of sensitivity during the runs, i.e., the used evolutionary algorithms do not enter a stage where they discover electrical drive designs that trade robustness for quality.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"2006 1","pages":"195-203"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86974650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Adriana Horelu, C. Leordeanu, E. Apostol, Dan Huru, M. Mocanu, V. Cristea
Forecasting has always been of interest. Whether one's field is finance, health or seismology, being able to predict future values based on previously gathered data proves to be invaluable when taking decisions concerning the future. In this paper, we research machine learning techniques for predictions on time series and choose the best models that fit our use case, Smart Farms, in which we distributedly analyze time series received from farm-monitoring sensors. On time series with short term dependencies, like temperature or pressure, we make predictions with Hidden Markov Models, whilst for those with long range dependencies, like ground wind speeds orprecipitations, we use Recurrent Neural Networks with Long Short-Term Memory architecture.
{"title":"Forecasting Techniques for Time Series from Sensor Data","authors":"Adriana Horelu, C. Leordeanu, E. Apostol, Dan Huru, M. Mocanu, V. Cristea","doi":"10.1109/SYNASC.2015.49","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.49","url":null,"abstract":"Forecasting has always been of interest. Whether one's field is finance, health or seismology, being able to predict future values based on previously gathered data proves to be invaluable when taking decisions concerning the future. In this paper, we research machine learning techniques for predictions on time series and choose the best models that fit our use case, Smart Farms, in which we distributedly analyze time series received from farm-monitoring sensors. On time series with short term dependencies, like temperature or pressure, we make predictions with Hidden Markov Models, whilst for those with long range dependencies, like ground wind speeds orprecipitations, we use Recurrent Neural Networks with Long Short-Term Memory architecture.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"29 1","pages":"261-264"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79289723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we introduce λR: A foundational calculus for sequence processing with regular expression types. Its term language is the lambda calculus extended with sequences of terms and its types are regular expressions over simple types. We provide a flexible notion of subtyping based on the semantic notion of nominal interpretation of a type. Then we prove that types are preserved by reduction (subject reduction), and that there exist no infinite reduction sequences starting at typed terms (strong normalization).
{"title":"Lambda Calculus with Regular Types","authors":"B. Dundua, Mário Florido, Temur Kutsia","doi":"10.1109/SYNASC.2015.29","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.29","url":null,"abstract":"In this paper we introduce λR: A foundational calculus for sequence processing with regular expression types. Its term language is the lambda calculus extended with sequences of terms and its types are regular expressions over simple types. We provide a flexible notion of subtyping based on the semantic notion of nominal interpretation of a type. Then we prove that types are preserved by reduction (subject reduction), and that there exist no infinite reduction sequences starting at typed terms (strong normalization).","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"370 ","pages":"129-136"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91519740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a general purpose cloud system efficiencies are yet to be had from supporting diverse application requirements within a heterogeneous storage system. Such a system poses significant technical challenges since storage systems are traditionally homogeneous. This paper uses the Ceph distributed file system, and in particular its concept of storage pools, to show how a storage solution can be partitioned to provide the heterogeneity needed to support the required application requirements.
{"title":"Supporting Heterogeneous Pools in a Single Ceph Storage Cluster","authors":"Stefan Meyer, J. Morrison","doi":"10.1109/SYNASC.2015.61","DOIUrl":"https://doi.org/10.1109/SYNASC.2015.61","url":null,"abstract":"In a general purpose cloud system efficiencies are yet to be had from supporting diverse application requirements within a heterogeneous storage system. Such a system poses significant technical challenges since storage systems are traditionally homogeneous. This paper uses the Ceph distributed file system, and in particular its concept of storage pools, to show how a storage solution can be partitioned to provide the heterogeneity needed to support the required application requirements.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"42 1","pages":"352-359"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75342415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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