Algorithmic Motion Planning and Related Geometric Problems on Parallel Machines (Dissertation Proposal)

The problem of algorithmic motion planning is one that has received considerable attention in recent years. The automatic planning of motion for a mobile object moving amongst obstacles is a fundamentally important problem with numerous applications in computer graphics and robotics. Numerous approximate techniques (AI-based, heuristics-based, potential field methods, for example) for motion planning have long been in existence, and have resulted in the design of experimental systems that work reasonably well under various special conditions [7, 29, 30]. Our interest in this problem, however, is in the use of algorithmic techniques for motion planning, with provable worst case performance guarantees. The study of algorithmic motion planning has been spurred by recent research that has established the mathematical depth of motion planning. Classical geometry, algebra, algebraic geometry and combinatorics are some of the fields of mathematics that have been used to prove various results that have provided better insight into the issues involved in motion planning [49]. In particular, the design and analysis of geometric algorithms has proved to be very useful for numerous important special cases. In the remainder of this proposal we will substitute the more precise term of algorithmic motion planning by just motion planning

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

Scaling Simulations of Reconfigurable Meshes.

This dissertation deals with reconfigurable bus-based models, a new type of parallel machine that uses dynamically alterable connections between processors to allow efficient communication and to perform fast computations. We focus this work on the Reconfigurable Mesh (R-Mesh), one of the most widely studied reconfigurable models. We study the ability of the R-Mesh to adapt an algorithm instance of an arbitrary size to run on a given smaller model size without significant loss of efficiency. A scaling simulation achieves this adaptation, and the simulation overhead expresses the efficiency of the simulation. We construct a scaling simulation for the Fusing-Restricted Reconfigurable Mesh (FR-Mesh), an important restriction of the R-Mesh. The overhead of this simulation depends only on the simulating machine size and not on the simulated machine size. The results of this scaling simulation extend to a variety of concurrent write rules and also translate to an improved scaling simulation of the R-Mesh itself. We present a bus linearization procedure that transforms an arbitrary non-linear bus configuration of an R-Mesh into an equivalent acyclic linear bus configuration implementable on an Linear Reconfigurable Mesh (LR-Mesh), a weaker version of the R-Mesh. This procedure gives the algorithm designer the liberty of using buses of arbitrary shape, while automatically translating the algorithm to run on a simpler platform. We illustrate our bus linearization method through two important applications. The first leads to a faster scaling simulation of the R-Mesh. The second application adapts algorithms designed for R-Meshes to run on models with pipelined optical buses. We also present a simulation of a Directional Reconfigurable Mesh (DR-Mesh) on an LR-Mesh. This simulation has a much better efficiency compared to previous work. In addition to the LR-Mesh, this simulation also runs on models that use pipelined optical buses

Parallel Geometric Algorithms.

Geometric algorithms have many important applications in science and technology. Some geometric problems require fast response time that could not be achieved by traditional sequential algorithms. However, the speed, power and versatility of parallel computers can be exploited to develop efficient geometric algorithms as shown in this dissertation. Our study focuses on designing efficient parallel geometric algorithms and analyzing their computational complexities. In this research, first we developed a parallel algorithm to find the maxima of a set of N points in the d-dimensional space, d $\u3e$ 3, on a hypercube SIMD machine. Our algorithm is a parallel implementation from the sequential algorithm given by Kung, Luccio, and Preparata (KLP75). Although the time complexity, O(N\sp{0.77}\log\sp{d-1}\ N), of our algorithm is not optimal, it is the first sublinear time algorithm for solving the high dimensional maxima problem. Next, we developed another parallel algorithm to construct the Voronoi diagram of a point set in the plane. Our algorithm is based on the sequential algorithm given by Brown (B79). We use an $N\times N$ mesh of trees (MOT) SIMD computer and get the optimal time complexity O(log\sp2N).. Finally, we developed another MOT algorithm to solve the congruent pattern problem. Given a simple polygon P with k edges and a planar graph G with N edges, $N\u3ek.$ The problem is to find all the patterns (cycles) in G which are congruent to P. Our algorithm is based on the CREW PRAM algorithm given by Jeong, Kim, and Baek (JKB92). We also use an $N\times N$ MOT and get the optimal time complexity $O(k\log N).$

The Monge array--an abstraction and its applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1991.Includes bibliographical references (p. 211-219).by James KIimbrough Park.Ph.D

Delaunay triangulation in R3 on the GPU

Ph.DDOCTOR OF PHILOSOPH

On expressing different concurrency paradigms on virtual execution environment

Virtual execution environments (VEE) such as the Java Virtual Machine (JVM) and the Microsoft Common Language Runtime (CLR) have been designed when the dominant computer architecture featured a Von-Neumann interface to programs: a single processor hiding all the complexity of parallel computations inside its design. Programs are expressed in an intermediate form that is executed by the VEE that defines an abstract computational model in which the concurrency model has been influenced by these design choices and it basically exposes the multi-threading model of the underlying operating system. Recently computer systems have introduced computational units in which concurrency is explicit and under program control. Relevant examples are the Graphical Processing Units (GPU such as Nvidia or AMD) and the Cell BE architecture which allow for explicit control of single processing unit, local memories and communication channels. Unfortunately programs designed for Virtual Machines cannot access to these resources since are not available through the abstractions provided by the VEE. A major redesign of VEEs seems to be necessary in order to bridge this gap. In this thesis we study the problem of exposing non-von Neumann computing resources within the Virtual Machine without need for a redesign of the whole execution infrastructure. In this work we express parallel computations relying on extensible meta-data and reflection to encode information. Meta-programming techniques are then used to rewrite the program into an equivalent one using the special purpose underlying architecture. We provide a case study in which this approach is applied to compiling Common Intermediate Language (CIL) methods to multi-core GPUs; we show that it is possible to access these non-standard computing resources without any change to the virtual machine design

Exploiting parallelism in n-D convex hull algorithms

PhD ThesisThe convex hull is a problem of primary importance because of its applications in computational geometry. A number of sequential and parallel algorithms for computing the convex hull of a finite set of points in the lower dimensions are known. In compar- ison, the general n-D problem is not as well understood and parallel algorithms are not so prevalent because the 2-D and 3-D methods are not easily extended to the general case. This thesis presents parallel algorithms for evaluating the general n- D convex hull problem (where 2-D and 3-D are special cases) using Swart's sequential algorithm. One of our methods combines a gift-wrapping technique with partitioning and merge algorithms > where the original list is split into p 1 partitions followed by the computation of the subhulls using the sequential n-D gift-wrapping method. The partial hulls are then combined using a fanin tree. The second method computes the convex hull in parallel by wrapping around the edges until a complete facial lattice structure of the polytope is generated. Several parameterised versions of the proposed algorithms have been implemented on the shared memory and message passing architectures. In the former, performance on an Encore Multimax using Encore Parallel Threads and the more lightweight Microthread programming utilities are examined. In the latter, performance on a transputer based machine using CS- Tools is discussed. We have shown that our techniques will be useful in the construction of faster algorithms which employ the n-D convex hull algorithms as a sub-algorithmCommonwealth Scholarship Commission in the United Kingdo