The Dataflow Computational Model And Its Evolution

Το υπολογιστικό μοντέλο dataflow είναι ένα εναλλακτικό του von-Neumann. Τα κυριότερα χαρακτηριστικά του είναι ο ασύγχρονος προγραμματισμός εργασιών και το ότι επιτρέπει μαζική παραλληλία. Αυτή η πτυχιακή είναι μία μελέτη αυτού του μοντέλου, καθώς και μερικών υβριδικών μοντέλων, που βρίσκονται ανάμεσα στο αρχικό μοντέλο dataflow και στο von-Neumann. Τέλος, υπάρχουν αναφορές σε μερικές αρχές του dataflow, οι οποίες έχουν υιοθετηθεί σε συμβατικές μηχανές, γλώσσες προγραμματισμού και συστήματα κατανεμημένων υπολογισμών.The dataflow computational model is an alternative to the von-Neumann model. Its most significant aspects are, that it is based on asynchronous instructions scheduling and exposes massive parallelism. This thesis is a review of the dataflow computational model, as well as of some hybrid models, which lie between the pure dataflow and the von Neumann model. Additionally, there are some references to dataflow principles, that are or are being adopted by conventional machines, programming languages and distributed computing systems

Efficient Sampling from Feasible Sets of SDPs and Volume Approximation

We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is geometric random walks. We analyze the arithmetic and bit complexity of certain primitive geometric operations that are based on the algebraic properties of spectrahedra and the polynomial eigenvalue problem. This study leads to the implementation of a broad collection of random walks for sampling from spectrahedra that experimentally show faster mixing times than methods currently employed either in theoretical studies or in applications, including the popular family of Hit-and-Run walks. The different random walks offer a variety of advantages , thus allowing us to efficiently sample from general probability distributions, for example the family of log-concave distributions which arise in numerous applications. We focus on two major applications of independent interest: (i) approximate the volume of a spectrahedron, and (ii) compute the expectation of functions coming from robust optimal control. We exploit efficient linear algebra algorithms and implementations to address the aforemen-tioned computations in very high dimension. In particular, we provide a C++ open source implementation of our methods that scales efficiently, for the first time, up to dimension 200. We illustrate its efficiency on various data sets

Sampling the feasible sets of SDPs and volume approximation

International audienceWe present algorithmic, complexity, and implementation results on the problem of sampling points in the interior and the boundary of a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is random walks. We define and analyze a set of primitive geometric operations that exploits the algebraic properties of spectrahedra and the polynomial eigenvalue problem, and leads to the realization of a broad collection of efficient random walks. We demonstrate random walks that experimentally show faster mixing time than the ones used previously for sampling from spectrahedra in theory or applications, for example Hit and Run. Consecutively, the variety of random walks allows us to sample from general probability distributions, for example the family of log-concave distributions which arise frequently in numerous applications. We apply our tools to compute (i) the volume of a spectrahedron and (ii) the expectation of functions coming from robust optimal control. We provide a C++ open source implementation of our methods that scales efficiently up to to dimension 200. We illustrate its efficiency on various data sets

Efficient Sampling from Feasible Sets of SDPs and Volume Approximation

We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is geometric random walks. We analyze the arithmetic and bit complexity of certain primitive geometric operations that are based on the algebraic properties of spectrahedra and the polynomial eigenvalue problem. This study leads to the implementation of a broad collection of random walks for sampling from spectrahedra that experimentally show faster mixing times than methods currently employed either in theoretical studies or in applications, including the popular family of Hit-and-Run walks. The different random walks offer a variety of advantages , thus allowing us to efficiently sample from general probability distributions, for example the family of log-concave distributions which arise in numerous applications. We focus on two major applications of independent interest: (i) approximate the volume of a spectrahedron, and (ii) compute the expectation of functions coming from robust optimal control. We exploit efficient linear algebra algorithms and implementations to address the aforemen-tioned computations in very high dimension. In particular, we provide a C++ open source implementation of our methods that scales efficiently, for the first time, up to dimension 200. We illustrate its efficiency on various data sets

Efficient sampling in spectrahedra and volume approximation

International audienceWe present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is, the feasible region of a semidefinite program.Our main tool is geometric random walks. We analyze the arithmetic and bit complexity of certain primitive geometric operations that are based on the algebraic properties of spectrahedra and the polynomial eigenvalue problem. This study leads to the implementation of a broad collection of random walks for sampling from spectrahedra that experimentally show faster mixing times than methods currently employed either in theoretical studies or in applications, including the popular family of Hit-and-Run walks. The different random walks offer a variety of advantages, thus allowing us to efficiently sample from general probability distributions, for example the family of log-concave distributions which arise in numerous applications. We focus on two major applications of independent interest: (i) approximate the volume of a spectrahedron, and (ii) compute the expectation of functions coming from robust optimal control.We exploit efficient linear algebra algorithms and implementations to address the aforementioned computations in very high dimension. In particular, we provide a C++ open source implementation of our methods that scales efficiently, for the first time, up to dimension 200. We illustrate its efficiency on various data sets