Zongyan Huang, M. England, J. Davenport, Lawrence Charles Paulson
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the human-made heuristic.
{"title":"Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition with Groebner Bases","authors":"Zongyan Huang, M. England, J. Davenport, Lawrence Charles Paulson","doi":"10.1109/SYNASC.2016.020","DOIUrl":"https://doi.org/10.1109/SYNASC.2016.020","url":null,"abstract":"Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the human-made heuristic.","PeriodicalId":268635,"journal":{"name":"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125492255","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}
This paper presents AUGURY, an application for the analysis of monitoring data from computers, servers or cloud infrastructures. The analysis is based on the extraction of patterns and trends from historical data, using elements of time-series analysis. The purpose of AUGURY is to aid a server administrator by forecasting the behaviour and resource usage of specific applications and in presenting a status report in a concise manner. AUGURY provides tools for identifying network traffic congestion and peak usage times, and for making memory usage projections. The application data processing specialises in two tasks: the parametrisation of the memory usage of individual applications and the extraction of the seasonal component from network traffic data. AUGURY uses a different underlying assumption for each of these two tasks. With respect to the memory usage, a limited number of single-valued parameters are assumed to be sufficient to parameterize any application being hosted on the server. Regarding the network traffic data, long-term patterns, such as hourly or daily exist and are being induced by work-time schedules and automatised administrative jobs. In this paper, the implementation of each of the two tasks is presented, tested using locally-generated data, and applied to data from weather forecasting applications hosted on a web server. This data is used to demonstrate the insight that AUGURY can add to the monitoring of server and cloud infrastructures.
{"title":"AUGURY: A Time Series Based Application for the Analysis and Forecasting of System and Network Performance Metrics","authors":"Nicolas Gutierrez, Manuela Wiesinger-Widi","doi":"10.1109/SYNASC.2016.062","DOIUrl":"https://doi.org/10.1109/SYNASC.2016.062","url":null,"abstract":"This paper presents AUGURY, an application for the analysis of monitoring data from computers, servers or cloud infrastructures. The analysis is based on the extraction of patterns and trends from historical data, using elements of time-series analysis. The purpose of AUGURY is to aid a server administrator by forecasting the behaviour and resource usage of specific applications and in presenting a status report in a concise manner. AUGURY provides tools for identifying network traffic congestion and peak usage times, and for making memory usage projections. The application data processing specialises in two tasks: the parametrisation of the memory usage of individual applications and the extraction of the seasonal component from network traffic data. AUGURY uses a different underlying assumption for each of these two tasks. With respect to the memory usage, a limited number of single-valued parameters are assumed to be sufficient to parameterize any application being hosted on the server. Regarding the network traffic data, long-term patterns, such as hourly or daily exist and are being induced by work-time schedules and automatised administrative jobs. In this paper, the implementation of each of the two tasks is presented, tested using locally-generated data, and applied to data from weather forecasting applications hosted on a web server. This data is used to demonstrate the insight that AUGURY can add to the monitoring of server and cloud infrastructures.","PeriodicalId":268635,"journal":{"name":"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117089628","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}