Time-Optimal Algorithms on Meshes With Multiple Broadcasting

The mesh-connected computer architecture has emerged as a natural choice for solving a large number of computational tasks in image processing, computational geometry, and computer vision. However, due to its large communication diameter, the mesh tends to be slow when it comes to handling data transfer operations over long distances. In an attempt to overcome this problem, mesh-connected computers have recently been augmented by the addition of various types of bus systems. One such system known as the mesh with multiple broadcasting involves enhancing the mesh architecture by the addition of row and column buses. The mesh with multiple broadcasting has proven to be feasible to implement in VLSI, and is used in the DAP family of computers. In recent years, efficient algorithms to solve a number of computational problems on meshes with multiple broadcasting have been proposed in the literature. The problems considered in this thesis are semigroup computations, sorting, multiple search, various convexity-related problems, and some tree problems. Based on the size of the input data for the problem under consideration, existing results can be broadly classified into sparse and dense. Specifically, for a given √n x √n mesh with multiple broadcasting, we refer to problems involving $m \in O(\sqrt{n}$) items as sparse, while the case £ O(n) will be referred to as dense. Finally, the case corresponding to 2 ≤ m ≤ n is be termed general. The motivation behind the current work is twofold. First, time-optimal solutions are proposed for the problems listed above. Secondly, an attempt is made to remove the artificial limitation of problems studied to sparse and dense cases. To establish the time-optimality of the algorithms presented in this work, we use some existing lower bound techniques along with new ones that we develop. We solve the semigroup computation problem for the general case and present a novel lower bound argument. We solve the multiple search problem in the general case and present some surprising applications to computational geometry. In the case of sorting, the general case is defined to be slightly different. For the specified range of the size of input, we present a time and VLSI-optimal algorithm. We also present time lower bound results and matching algorithms for a number of convexity related and tree problems in the sparse case

A Computational Paradigm on Network-Based Models of Computation

The maturation of computer science has strengthened the need to consolidate isolated algorithms and techniques into general computational paradigms. The main goal of this dissertation is to provide a unifying framework which captures the essence of a number of problems in seemingly unrelated contexts in database design, pattern recognition, image processing, VLSI design, computer vision, and robot navigation. The main contribution of this work is to provide a computational paradigm which involves the unifying framework, referred to as the multiple Query problem, along with a generic solution to the Multiple Query problem. To demonstrate the applicability of the paradigm, a number of problems from different areas of computer science are solved by formulating them in this framework. Also, to show practical relevance, two fundamental problems were implemented in the C language using MPI. The code can be ported onto many commercially available parallel computers; in particular, the code was tested on an IBM-SP2 and on a network of workstations

Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

Second Generation General System Theory: Perspectives in Philosophy and Approaches in Complex Systems

Following the classical work of Norbert Wiener, Ross Ashby, Ludwig von Bertalanffy and many others, the concept of System has been elaborated in different disciplinary fields, allowing interdisciplinary approaches in areas such as Physics, Biology, Chemistry, Cognitive Science, Economics, Engineering, Social Sciences, Mathematics, Medicine, Artificial Intelligence, and Philosophy. The new challenge of Complexity and Emergence has made the concept of System even more relevant to the study of problems with high contextuality. This Special Issue focuses on the nature of new problems arising from the study and modelling of complexity, their eventual common aspects, properties and approaches—already partially considered by different disciplines—as well as focusing on new, possibly unitary, theoretical frameworks. This Special Issue aims to introduce fresh impetus into systems research when the possible detection and correction of mistakes require the development of new knowledge. This book contains contributions presenting new approaches and results, problems and proposals. The context is an interdisciplinary framework dealing, in order, with electronic engineering problems; the problem of the observer; transdisciplinarity; problems of organised complexity; theoretical incompleteness; design of digital systems in a user-centred way; reaction networks as a framework for systems modelling; emergence of a stable system in reaction networks; emergence at the fundamental systems level; behavioural realization of memoryless functions