Theoretical Computing Research Articles

Optimal Parallel Algorithms for Computing the Sum, the Prefix-Sums, and the Summed Area Table on the Memory Machine Models

The main contribution of this paper is to show optimal parallel algorithms to compute the sum, the prefix-sums, and the summed area table on two memory machine models, the Discrete Memory Machine (DMM) and the Unified Memory Machine (UMM). The DMM and the UMM are theoretical parallel computing models that capture the essence of the shared memory and the global memory of GPUs. These models have three parameters, the number p of threads, and the width w of the memory, and the memory access latency l. We first show that the sum of n numbers can be computed in O( n w + nl p + l log n) time units on the DMM and the UMM. We then go on to show that Ω(n w + nl p + l log n) time units are necessary to compute the sum. We also present a parallel algorithm that computes the prefix-sums of n numbers in O( n w + nl p + l log n) time units on the DMM and the UMM. Finally, we show that the summed area table of size √ n × √n can be computed in O( n w + nl p + l log n) time units on the DMM and the UMM. Since the computation of the prefix-sums and the summed area table is at least as hard as the sum computation, these parallel algorithms are also optimal. key words: Memory machine models, prefix-sums computation, parallel algorithm, GPU, CUDA

Cross-Platform Mobile App Software Development in the Curriculum

Introduction Since its introduction in 2007, the Apple iPhone has changed our perception of how mobile phones should look and how consumers use them. At the same time the iPhone has helped to make Apple the most valuable company in America. However, even with its runaway commercial success, the Apple iPhone is not the current smartphone market share leader. Heavy competition from Google Microsoft Windows Phone, and Research in Motion Blackberry, along with fickle consumers, keep the smartphone market from being dominated by a single platform. Recent statistics from market intelligence company comScore listed the U.S. Smartphone platform market share for January 2012 as 48.6% for Google 29.% for Apple iOS, 15.2% RIM Blackberry, and 4.4% Microsoft Windows Phone (comScore Reveals, 2012). As an indicator of how quickly market share can change, the low market share for Windows Phone is predicted to increase to 20.9% by 2015 (IDC: Android, 2012). No clear platform leader does present a conundrum for professional software developers as each mobile device platform maker provides software development tools for their platform. Because the vendor's tools have little in common, an app that runs on multiple smartphone platforms must be written for each of those platforms. Choosing a mobile platform and toolset is especially difficult for educators who have little free time to become skilled on any one platform, let alone several. The Department of Computer and Information Technology at Purdue University in West Lafayette, Indiana has offered courses in app development for mobile devices since Fall 2002. Each semester all students have been required to write code using the native app developer tools provided by the platform vendor. During the Fall 2011 semester I am trying a new approach of using cross-platform mobile app development tools which should allow students to develop apps for the platform of their choosing. In this paper, I discuss my experiences teaching with these tools including an overview of how apps can be built using these cross-platform technologies, our course pedagogy, the learning topics we covered, problems we encountered, and our recommendations for others considering the same approach. Background By design, the curriculum in the Department of Computer and Information Technology (CIT) at Purdue University in West Lafayette, Indiana is focused on the application of Information Technology (IT) rather than on theoretical computing. To this end, CIT's course learning objectives are designed so students learn through hands-on, practical experience. This characteristic differentiates our courses from those of the Computer Science (CS) or Electrical and Computer Engineering (ECE) departments, which are more theoretical based. The typical student progression through our curriculum includes a minimum background of three programming courses, including an introductory course using C#, a web application development course using HTML and C#, and an intermediate object-oriented programming course using Java (Harriger, Lutes, & Purdum, 2007). I have been teaching mobile app development courses for CIT beginning in the Fall 2002 semester. These courses, CIT 355 Software Development for Mobile Devices 1 and CIT 425 Software Development for Mobile Devices 2 (Lutes, 2004), have proven to be popular and have been offered nearly every semester since. The typical student is a junior or senior majoring in CIT. Occasionally undergraduate and graduate students from other related disciplines such as CS, ECE, and Computer Graphics also take the courses. Typical enrollment figures are between 12 and 20 students per semester. The enrollment numbers are limited by the number of workstations and mobile devices in our department's mobile computing laboratory. My original goal for developing these courses was simply to motivate more students to choose careers in software development. …

Dynamical analysis of clustering-based wireless sensor networks

In wireless sensor networks (WSNs), clustering-based algorithms have been proved to be effective techniques to save energy and improve fault tolerance. In this paper, a scale-free evolving model for clustering-based WSNs with exponential growth behavior is presented, in which the nodes arrive as a Poisson process with rate λ. This model takes into account four types of evolving events: selection of cluster-head nodes, preferential attachment of non cluster-head nodes, failure of non cluster-head nodes, transition of non cluster-head nodes. By using continuum theory, the theoretical computing and simulated results show that the size distribution of cluster in this model follows a power law. The scale-free properties revealed in this model display a tempting application foreground. Key words: Wireless sensor networks, continuum theory, scale-free, exponential growth behavior.

Dynamics of Wireless Sensor Networks

Power-Law topology has been proved to be an effective technique to improve fault tolerance. With the motivation of construct reliable topology for wireless sensor networks, a Power-Law Evolving Model (PLEW) of wireless sensor networks by stochastic placement is proposed in this article. In a dynamic evolving process of Wireless Sensor Networks, there are four types of events as follows: adding new nodes, nodes failure, adding new links, and links failure. The dynamics of nodes and links are integrated into the evolving model consequently. By using the continuum theory, the theoretical computing and simulated results show that the degree distribution of this model follows a power law. The scale-free properties revealed in this model can be applied into the scenarios required high dependability, such as national defense or survivability systems.

Study of GaN-Based Light-Emitting Diodes Grown on Chemical Wet-Etching-Patterned Sapphire Substrate With V-Shaped Pits Roughening Surfaces

We investigate the mechanism responding for performance enhancement of gallium nitride (GaN)-based light-emitting diode (LED) grown on chemical wet-etching-patterned sapphire substrate (CWE-PSS) with V-Shaped pit features on the top surface. According to temperature-dependent photoluminescence (PL) measurement and the measured external quantum efficiency, the structure can simultaneously enhance both internal quantum efficiency and light extraction efficiency. Comparing to devices grown on planar sapphire substrate, the threading dislocation defects of LED grown on CWE-PSS are reduced from 1.28 times 109/cm2 to 3.62 times 108/cm2, leading to a 12.5% enhancement in internal quantum efficiency. In terms of the theoretical computing of radiation patterns, the V-Shaped pits roughening surface can be thought of as a strong diffuser with paraboloidal autocorrelation function, increasing the escape probability of trapped photons and achieving a 20% enhancement in light extraction efficiency. Moreover, according to the measurement of optical diffraction power, CWE-PSS demonstrated superior guided light extraction efficiency than that of planar sapphire substrate, thus an extra 7.8% enhancement in light extraction efficiency was obtained. Therefore, comparing to the conventional LED, an overall 45% enhancement in integrated output power was achieved.

Thirdness as self-reference in computing

We argue that the essence of thirdness in computing is self-reference. Our discussion is grounded on the theories of Church and Curry, which have been studied in the domain of theoretical computing. Using their theories, we show that any program can be transformed into a program consisting only of three-term relations, where the essence of the three-term relations lies in self-reference.

A Multiplatform Methodology: Developing Mobile Device Applications

When the Electrical and Computer Engineering Department at the American University of Beirut decided to launch a computing course on mobile computing devices, the author designed a course to meet industry requirements and to introduce students to the major platforms used to build practical applications. He dedicated much of Pervasive Computing Systems and Applications, EECE 679, to teaching mobile device application programming through code demonstrations and in-class application building. The course also covered front-end mobile device technologies and back-end infrastructures. Today, many pervasive computing courses focus on research and theory. Those that do deal with developing mobile applications often limit their coverage to a specific platform. This course covers practical and theoretical pervasive computing, lets students acquire hands-on application-building experience in multiple platforms, and acquaints students with recent developments in related technologies and research. The course includes a mix of lectures, code demonstrations, and student presentations.

TAKING IT ON TRUST: REASON AND OBSERVABILITY IN QUANTUM COMPUTING

If quantum computing is located somewhere between physics and theoretical computing, a basic question concerns which characteristic features are derived from the latter. From a logical point of view, the concept of computation provides a definition of the natural process of calculare. It rests on trust that a procedure of reason can be reproduced mechanically. Turing argues for the adequacy of the concept by introducing a requirement of "observability," which is expressed through finiteness and locality conditions. However, according to the uncertainty principle, no computational path can be observed. How does quantum computing contend with Turing's constraints? What observables are relevant to the computation? This is an attempt to sharpen such questions.

Beyond Factorization and Search

Recent theoretical developments have driven the search for computers based on the unusual rules of quantum mechanics. In his Perspective, Grover reviews the progress in theoretical quantum computing, with particular focus on search algorithms and applications to difficult computational problems.

Computational Aspects of Pathology Image Classification and Retrieval

We are investigating the role of high performance computing for support of a comprehensive pathology image atlas. The primary computing component is a database access mechanism providing retrieval by content based image matching (CBIR) along with traditional term based queries. An organization based on information theoretic and Bayesian principles using decision trees and signature files is being developed. The essential role of HPC is the discovery, selection, and optimization of medically useful image feature sets via genetic algorithm and simulated annealing methods. This paper outlines the problem area along with aspects of the underlying theoretical basis and distinguishing computing characteristics. Efficiency of key portions of the computations can be greatly improved by using parallelism within the computer word length using bit counting instructions to implement voting and multimedia style instruction sets for low level image processing.

Theoretical computing

Journal of Logic and Computation. Editor-in-chief D. M. Gabbay. Oxford University Press. 6/yr. Europe £115, elsewhere $215 (Institutional); Europe £55, elsewhere $99 (personal). Applicable Algebra in Engineering, Communication and Computing. Managing Editor Jacques Calmet. Springer. 4/yr. DM258, $161. Parallel Processing Letters. Editor M. Cosnard. World Scientific. 4/yr. $180 (Institutional); $90 (personal, and institutions from developing countries).

Topology of the view complex

In this paper we consider a family of simplicial complexes, which we call the view complexes. Our choice of objects of study is motivated by theoretical distributed computing, since the view complex is a key simplicial construction used for protocol complexes in the snapshot computational model. We show that the view complex $\view$ can be collapsed to the well-known complex $\chi(\Delta^n)$, called standard chromatic subdivision of a simplex, and that $\chi(\Delta^n)$ is itself collapsible. Furthermore, we show that the collapses can be performed simultaneously in entire orbits of the natural symmetric group action. Our results yield a purely combinatorial and constructive understanding of the topology of view complexes, at the same time as they enhance our knowledge about the standard chromatic subdivision of a simplex.