Catamorphisms are a class of higher-order functions that recursively traverse an inductive data structure to produce a value. An important result related to catamorphisms is the fusion theorem, which gives sufficient conditions to rewrite compositions of catamorphisms. We use the Coq proof assistant to automatically define a catamorphism and a fusion theorem according to an arbitrary inductive type definition. Catamorphisms are then used to define functional specifications and the fusion theorem is applied to derive efficient programs that match those specifications.
{"title":"Catamorphism Generation and Fusion Using Coq","authors":"Simon Robillard","doi":"10.1109/SYNASC.2014.32","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.32","url":null,"abstract":"Catamorphisms are a class of higher-order functions that recursively traverse an inductive data structure to produce a value. An important result related to catamorphisms is the fusion theorem, which gives sufficient conditions to rewrite compositions of catamorphisms. We use the Coq proof assistant to automatically define a catamorphism and a fusion theorem according to an arbitrary inductive type definition. Catamorphisms are then used to define functional specifications and the fusion theorem is applied to derive efficient programs that match those specifications.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131353288","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 propose an architecture for a storage system of surveillance videos. Such systems have to handle massive amounts of incoming video streams and relatively few requests for replay. In such a system load (i.e., Write requests) scheduling is essential to guarantee performance. Large-scale data-storage system (LSDSS) is an emerging hosting facility for video-storage, which has a very high number of writes while most of the videos are never or rarely watched. We discuss the design and implementation of LSDSS and load scheduling in autonomous storage environments called datacenters in LSDSS. A datacenter (DC) is the basic concept in our LSDSS, which has the self-management system to store data efficiently. A LSDSS consists of many DCs organized in a hierarchy fashion, thereby decentralizing load scheduling tasks. Because DC has a simple design, load scheduling is particularly suited for implementation on a real-time video surveillance and allows to make scheduling decisions. We also discuss experimental results that clearly show the advantage of load scheduling over the widely known base load scheduling.
{"title":"Load Scheduling in a Cloud Based Massive Video-Storage Environment","authors":"K. Bayyapu, Paul F. Fischer","doi":"10.1109/SYNASC.2014.54","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.54","url":null,"abstract":"We propose an architecture for a storage system of surveillance videos. Such systems have to handle massive amounts of incoming video streams and relatively few requests for replay. In such a system load (i.e., Write requests) scheduling is essential to guarantee performance. Large-scale data-storage system (LSDSS) is an emerging hosting facility for video-storage, which has a very high number of writes while most of the videos are never or rarely watched. We discuss the design and implementation of LSDSS and load scheduling in autonomous storage environments called datacenters in LSDSS. A datacenter (DC) is the basic concept in our LSDSS, which has the self-management system to store data efficiently. A LSDSS consists of many DCs organized in a hierarchy fashion, thereby decentralizing load scheduling tasks. Because DC has a simple design, load scheduling is particularly suited for implementation on a real-time video surveillance and allows to make scheduling decisions. We also discuss experimental results that clearly show the advantage of load scheduling over the widely known base load scheduling.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116259870","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}
Computations with sparse matrices are widespread in scientific projects. Used data format affects strongly the performance and also the space-efficiency. Commonly used storage formats (such as COO or CSR) are not suitable neither for some numerical algebra operations (e.g., The sparse matrix-vector multiplication) due to the required indirect addressing nor for I/O file operations with sparse matrices due to their high space complexities. In our previous papers, we prove that the idea of using the quad tree for these purposes is viable. In this paper, we present a completely new algorithm based on bottom-up approach for the converting matrices from common storage formats to the quad tree format. We derive the asymptotic complexity of our new algorithm, design the parallel variant of the classical and the new algorithm, and discuss their performance.
{"title":"Efficient Converting of Large Sparse Matrices to Quadtree Format","authors":"I. Šimeček, D. Langr, Jan Trdlicka","doi":"10.1109/SYNASC.2014.25","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.25","url":null,"abstract":"Computations with sparse matrices are widespread in scientific projects. Used data format affects strongly the performance and also the space-efficiency. Commonly used storage formats (such as COO or CSR) are not suitable neither for some numerical algebra operations (e.g., The sparse matrix-vector multiplication) due to the required indirect addressing nor for I/O file operations with sparse matrices due to their high space complexities. In our previous papers, we prove that the idea of using the quad tree for these purposes is viable. In this paper, we present a completely new algorithm based on bottom-up approach for the converting matrices from common storage formats to the quad tree format. We derive the asymptotic complexity of our new algorithm, design the parallel variant of the classical and the new algorithm, and discuss their performance.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"142 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114434703","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}
Fuzzy automata have been proposed in late 1960's, being among the firsts domains extended through the framework of fuzzy logic. Fuzzy automata (FA) are fuzzy logic extensions of classic, or crisp automata. Despite their long existence, fuzzy automata have quite few real-life applications, most of them related to fuzzy languages, while crisp automata are applied in many devices that are part of our everyday life, from coffee machines to ATMs. In this paper we continue our previous work of investigating by VHDL simulation the performance of fuzzy automata. The new aspect compared to our previous work is the focus on the applications of FA.
{"title":"Performance Evaluation of Fuzzy Automata Using VHDL Simulation","authors":"Daniel Butoianu, Doru Todinca","doi":"10.1109/SYNASC.2014.34","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.34","url":null,"abstract":"Fuzzy automata have been proposed in late 1960's, being among the firsts domains extended through the framework of fuzzy logic. Fuzzy automata (FA) are fuzzy logic extensions of classic, or crisp automata. Despite their long existence, fuzzy automata have quite few real-life applications, most of them related to fuzzy languages, while crisp automata are applied in many devices that are part of our everyday life, from coffee machines to ATMs. In this paper we continue our previous work of investigating by VHDL simulation the performance of fuzzy automata. The new aspect compared to our previous work is the focus on the applications of FA.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122173382","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}
Petru Florin Mihancea, Edit Mercedes Mera-Batiz, M. Minea
Automatic generation of a good test suite is difficult, especially for object-oriented software. Feedback-directed random test generation is an approach that can achieve good branch coverage and has been used as a basis to systematically construct suites for testing realistic Java programs. We augment this random test generation method to create tests suites that satisfy an intra-class data-flow coverage criterion which is highly relevant for object orientation, although little addressed or achieved by tools in practice. We show that our approach can be used on real object-oriented software and that the technique for guiding test generation produces an increase in coverage.
{"title":"Guiding Random Test Generation for Intra-class Dataflow Coverage","authors":"Petru Florin Mihancea, Edit Mercedes Mera-Batiz, M. Minea","doi":"10.1109/SYNASC.2014.28","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.28","url":null,"abstract":"Automatic generation of a good test suite is difficult, especially for object-oriented software. Feedback-directed random test generation is an approach that can achieve good branch coverage and has been used as a basis to systematically construct suites for testing realistic Java programs. We augment this random test generation method to create tests suites that satisfy an intra-class data-flow coverage criterion which is highly relevant for object orientation, although little addressed or achieved by tools in practice. We show that our approach can be used on real object-oriented software and that the technique for guiding test generation produces an increase in coverage.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127689258","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}
The present author, Inaba and Kako proposed local blocking in a recent paper [6], for solving parametric sparse linear systems appearing in industry, so that the obtained solution is suited for determining optimal parameter values. They employed a graph theoretical treatment, and the points of their method are to select strongly connected sub graphs satisfying several restrictions and to form the so-called "characteristic system". The method of selecting sub graphs is, however, complicated and seems to be unsuited for big systems. In this paper, assuming that a small number of representative vertices of the characteristic system are specified by the user, we give a simple method of finding a characteristic system. Then, we present a simple and satisfactory method of decomposing the given graph into strongly connected sub graphs. The method applies the SCC (strongly connected component) decomposition algorithm. The complexity of new method is O(# (vertex) +# (edge)). We test our method successfully by three graphs of 100 vertices made artificially showing different but typical features.
{"title":"Solving Parametric Sparse Linear Systems by Local Blocking, II","authors":"Tateaki Sasaki, D. Inaba, F. Kako","doi":"10.1145/2733693.2733712","DOIUrl":"https://doi.org/10.1145/2733693.2733712","url":null,"abstract":"The present author, Inaba and Kako proposed local blocking in a recent paper [6], for solving parametric sparse linear systems appearing in industry, so that the obtained solution is suited for determining optimal parameter values. They employed a graph theoretical treatment, and the points of their method are to select strongly connected sub graphs satisfying several restrictions and to form the so-called \"characteristic system\". The method of selecting sub graphs is, however, complicated and seems to be unsuited for big systems. In this paper, assuming that a small number of representative vertices of the characteristic system are specified by the user, we give a simple method of finding a characteristic system. Then, we present a simple and satisfactory method of decomposing the given graph into strongly connected sub graphs. The method applies the SCC (strongly connected component) decomposition algorithm. The complexity of new method is O(# (vertex) +# (edge)). We test our method successfully by three graphs of 100 vertices made artificially showing different but typical features.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127801600","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}
Hereditarily binary numbers are a tree-based number representation derived from a bijection between natural numbers and iterated applications of two simple functions corresponding to bijective base 2 numbers. This paper describes several new arithmetic algorithms on hereditarily binary numbers that, while within constant factors from their traditional counterparts for their average case behavior, make tractable important computations that are impossible with traditional number representations.
{"title":"New Arithmetic Algorithms for Hereditarily Binary Natural Numbers","authors":"Paul Tarau","doi":"10.1109/SYNASC.2014.23","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.23","url":null,"abstract":"Hereditarily binary numbers are a tree-based number representation derived from a bijection between natural numbers and iterated applications of two simple functions corresponding to bijective base 2 numbers. This paper describes several new arithmetic algorithms on hereditarily binary numbers that, while within constant factors from their traditional counterparts for their average case behavior, make tractable important computations that are impossible with traditional number representations.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114479209","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, enhanced gradient descent learning algorithms for complex-valued feed forward neural networks are proposed. The most known such enhanced algorithms for real-valued neural networks are: quick prop, resilient back propagation, delta-bar-delta, and Super SAB, and so it is natural to extend these learning methods to complex-valued neural networks, also. The complex variants of these four algorithms are presented, which are then exemplified on various function approximation problems, as well as on channel equalization and time series prediction applications. Experimental results show an important improvement in training and testing error over classical gradient descent and gradient descent with momentum algorithms.
{"title":"Enhanced Gradient Descent Algorithms for Complex-Valued Neural Networks","authors":"Călin-Adrian Popa","doi":"10.1109/SYNASC.2014.44","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.44","url":null,"abstract":"In this paper, enhanced gradient descent learning algorithms for complex-valued feed forward neural networks are proposed. The most known such enhanced algorithms for real-valued neural networks are: quick prop, resilient back propagation, delta-bar-delta, and Super SAB, and so it is natural to extend these learning methods to complex-valued neural networks, also. The complex variants of these four algorithms are presented, which are then exemplified on various function approximation problems, as well as on channel equalization and time series prediction applications. Experimental results show an important improvement in training and testing error over classical gradient descent and gradient descent with momentum algorithms.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122049897","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}
M. Rostami, H. M. Bucker, C. Vogt, Ralf Seidler, David Neuhauser, V. Rath
Inverse problems arise in various areas of science and engineering. These problems are not only difficult to solve numerically, but they also require a large amount of computer resources both in time and memory. It is therefore not surprising that inverse problems are often solved using techniques from high-performance computing. We consider the parallelization of an inverse problem in the field of geothermal reservoir engineering. In this particular scientific application, the underlying software package is already parallelized using the shared-memory programming paradigm Open MP. Here, we present an extension of this parallelization to distributed memory enabling a hybrid Open MP/MPI parallelization. The situation is different from the standard way of hybrid parallel programming because the data structures of the Open MP-parallelized code differ from those in the serial implementation. We exploit this transformation of the data structures in our distributed-memory strategy for parallelizing an ensemble Kalman filter, a particular method for the solution of inverse problems. We describe this novel parallelization strategy, introduce a performance model, and present timing results on a compute cluster using nodes with 2 sockets, each equipped with Intel Xeon X5675 Westmere EP processors with 6 cores. All timing results are obtained with a pure MPI parallelization without using any Open MP threads.
逆问题出现在科学和工程的各个领域。这些问题不仅在数值上难以解决，而且在时间和内存上都需要大量的计算机资源。因此，通常使用高性能计算技术来解决逆问题并不奇怪。本文研究了地热储层工程领域中一个反问题的并行化问题。在这个特殊的科学应用程序中，底层软件包已经使用共享内存编程范例Open MP并行化了。在这里，我们将这种并行化扩展到分布式内存，从而实现Open MP/MPI混合并行化。这种情况与混合并行编程的标准方式不同，因为Open mp并行代码的数据结构与串行实现中的数据结构不同。我们在分布式存储策略中利用这种数据结构的转换来并行化集成卡尔曼滤波器，这是一种求解逆问题的特殊方法。我们描述了这种新的并行化策略，介绍了一个性能模型，并在一个使用2个插槽的节点的计算集群上给出了时序结果，每个节点配备了Intel Xeon X5675 Westmere EP 6核处理器。所有计时结果都是通过纯MPI并行化获得的，而不使用任何Open MP线程。
{"title":"A Distributed-Memory Parallelization of a Shared-Memory Parallel Ensemble Kalman Filter","authors":"M. Rostami, H. M. Bucker, C. Vogt, Ralf Seidler, David Neuhauser, V. Rath","doi":"10.1109/SYNASC.2014.67","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.67","url":null,"abstract":"Inverse problems arise in various areas of science and engineering. These problems are not only difficult to solve numerically, but they also require a large amount of computer resources both in time and memory. It is therefore not surprising that inverse problems are often solved using techniques from high-performance computing. We consider the parallelization of an inverse problem in the field of geothermal reservoir engineering. In this particular scientific application, the underlying software package is already parallelized using the shared-memory programming paradigm Open MP. Here, we present an extension of this parallelization to distributed memory enabling a hybrid Open MP/MPI parallelization. The situation is different from the standard way of hybrid parallel programming because the data structures of the Open MP-parallelized code differ from those in the serial implementation. We exploit this transformation of the data structures in our distributed-memory strategy for parallelizing an ensemble Kalman filter, a particular method for the solution of inverse problems. We describe this novel parallelization strategy, introduce a performance model, and present timing results on a compute cluster using nodes with 2 sockets, each equipped with Intel Xeon X5675 Westmere EP processors with 6 cores. All timing results are obtained with a pure MPI parallelization without using any Open MP threads.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122119184","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 continue the Coxeter spectral study of finite connected loop-free edge-bipartite graphs Δ, with m+2 ≥ 3 vertices (a class of signed graphs), started in [SIAM J. Discrete Math., 27(2013), 827-854] by means of the complex Coxeter spectrum speccΔ ⊆ C and presented in our talks given in SYNASC12 and SYNASC13. Here, we study non-negative edge-bipartite graphs of corank two, in the sense that the symmetric Gram matrix GΔ ∈ Mm+2(Z) of Δ is positive semi-definite of rank m ≥ 1. Extending each of the simply laced Euclidean diagrams Am, m ≥ 1, Dm, m ≥ 4, Ẽ6, Ẽ7, Ẽ8 by one vertex, we construct a family of loop-free corank two diagrams Ãm2, D̃m2, Ẽ62, Ẽ72, Ẽ82 (called simply extended Euclidean diagrams) such that they classify all connected corank two loop-free edge-bipartite graphs Δ, with m + 2 ≥ 3 vertices, up to Z-congruence Δ ~z Δ'. Here Δ ~z Δ' means that GΔ', = Btr ·GΔ ·B, for some B ∈ Mm+2(Z) such that det B = ±1. We present algorithms that generate all such edge-bipartite graphs of a given size m + 2 ≥ 3, together with their Coxeter polynomials, and the reduced Coxeter numbers, using symbolic and numeric computer calculations in Python. Moreover, we prove that for any corank two connected loop-free edge-bipartite graph Δ, with m + 2 ≥ 3 vertices, there exists a simply extended Euclidean diagram D such that Δ ~z D.
{"title":"On Corank Two Edge-Bipartite Graphs and Simply Extended Euclidean Diagrams","authors":"Marcin Gąsiorek, D. Simson, Katarzyna Zając","doi":"10.1109/SYNASC.2014.17","DOIUrl":"https://doi.org/10.1109/SYNASC.2014.17","url":null,"abstract":"We continue the Coxeter spectral study of finite connected loop-free edge-bipartite graphs Δ, with m+2 ≥ 3 vertices (a class of signed graphs), started in [SIAM J. Discrete Math., 27(2013), 827-854] by means of the complex Coxeter spectrum specc<sub>Δ</sub> ⊆ C and presented in our talks given in SYNASC12 and SYNASC13. Here, we study non-negative edge-bipartite graphs of corank two, in the sense that the symmetric Gram matrix G<sub>Δ</sub> ∈ M<sub>m+2</sub>(Z) of Δ is positive semi-definite of rank m ≥ 1. Extending each of the simply laced Euclidean diagrams A<sub>m</sub>, m ≥ 1, D<sub>m</sub>, m ≥ 4, Ẽ<sub>6</sub>, Ẽ<sub>7</sub>, Ẽ<sub>8</sub> by one vertex, we construct a family of loop-free corank two diagrams Ã<sub>m</sub><sup>2</sup>, D̃<sub>m</sub><sup>2</sup>, Ẽ<sub>6</sub><sup>2</sup>, Ẽ<sub>7</sub><sup>2</sup>, Ẽ<sub>8</sub><sup>2</sup> (called simply extended Euclidean diagrams) such that they classify all connected corank two loop-free edge-bipartite graphs Δ, with m + 2 ≥ 3 vertices, up to Z-congruence Δ ~z Δ'. Here Δ ~z Δ' means that G<sub>Δ'</sub>, = B<sup>tr</sup> ·G<sub>Δ</sub> ·B, for some B ∈ M<sub>m+2</sub>(Z) such that det B = ±1. We present algorithms that generate all such edge-bipartite graphs of a given size m + 2 ≥ 3, together with their Coxeter polynomials, and the reduced Coxeter numbers, using symbolic and numeric computer calculations in Python. Moreover, we prove that for any corank two connected loop-free edge-bipartite graph Δ, with m + 2 ≥ 3 vertices, there exists a simply extended Euclidean diagram D such that Δ ~z D.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130178122","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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