Theory Of Parallel Computing Research Articles

Some aspects of the organization of information security of functioning of multiprocessor computing systems

The subject of the research is to improve the features of the organization of information security of multiprocessor computing systems. The goal of this work is to identify and implement measures to secure information that can be effective when using multiprocessor modular computing systems or in parallel calculations on multithreaded systems. To achieve this goal, the following tasks are solved: comparison of data protection methods in multiprocessor and sequential systems, as well as study of the specifics of applying various cryptographic methods to the methods of implementing protection; in accordance with some aspects of constructing multiprocessor systems, consideration and identification of key elements that require special attention in the development of a security system; to show that the main choice of data protection methods in multiprocessor systems is determined by differences from sequential systems in the theoretical and hardware implementation. The methods used are: main provisions of the theory of computing systems, theory of parallel computing, theory of the construction of operating systems, methods and algorithms for data protection. The following results were obtained. The main aspects in definition and use of information protection measures that can be effective when using multiprocessor modular computing systems or in parallel calculations on multithreaded systems are identified. Comparison of methods of data protection with sequential systems is carried out, and also the influence of application of various cryptographic methods on methods of data protection implementation is considered. It is shown that the main choice of data protection methods in multiprocessor systems is determined by differences from sequential systems in theoretical and hardware implementation. The conclusions . In accordance with some aspects of the construction of multiprocessor systems, the key elements that require special attention in the development of a security system are examined and identified. The paper shows that a parallel system requires both more hardware and software, and with each additional calculation module the system becomes more complex. And this, in turn, further complicates the protection system as a whole, which may entail some slowdown in the execution of application programs with the help of multiprocessor computing systems. However, in the long term, the proposed approach makes it possible to provide increased security for the operation of multiprocessor systems. To protect data in such systems, a number of methods are considered and analyzed.

On Computing Maximal Independent Sets of Hypergraphs in Parallel

Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing. Essentially, the challenge is to design (randomized) algorithms in which the number of processors used is polynomial and the (expected) runtime is polylogarithmic in the size of the input. Unlike the well-understood case of MIS in graphs, for the hypergraph problem, our knowledge is quite limited despite considerable work. It is known that the problem is in RNC when the edges of the hypergraph have constant size. For general hypergraphs with n vertices and m edges, the fastest previously known algorithm works in time O (√ n ) with poly( m,n ) processors. In this article, we give an EREW PRAM randomized algorithm that works in time n o (1) with O ( n + mlog n ) processors on general hypergraphs satisfying m ≤ n o (1) log log n /log log log n . We also give an EREW PRAM deterministic algorithm that runs in time n ϵ on a graph with m ≤ n 1/δ edges, for any constants δ, ϵ; the number of processors is polynomial in m, n for a fixed choice of δ, ϵ. Our algorithms are based on a sampling idea that reduces the dimension of the hypergraph and employs the algorithm for constant dimension hypergraphs as a subroutine.

Point Cloud Registrational Computing Based on Hadoop

For the problem of huge computation and requiring high computing resource in point cloud registration, according to the theory of parallel computing, the algorithm of point cloud registration base on MapReduce is designed. Through building a Hadoop cluster consisted by average PCs, four examples have been tested. The experiment results show that point cloud registration algorithm based on MapReduce can register point cloud data with high accuracy.

An Energy Efficient and Load Balancing Distributed Image Compression Algorithm in WMSNs

According to the problem that resource-constrained always restricts image transmission in the wireless multimedia sensor networks (WMSNs), this paper combines with theory of parallel computing and puts forward a kind of energy efficient and load balancing distributed image compression algorithm based on the JPEG2000. The algorithm introduces node competitive factor and communication cost function for the purpose of making the most of the limited resource to transmit more images and maintaining load balancing in the image compression process. In addition, the algorithm encodes the information separately which is divided accord to the frequency after wavelet transform, in order to relieve the load of the cluster head and prolong the network life time. Further simulations demonstrate that the algorithm can ensure a certain quality of the reconstructed image, reduce 30% energy consumption of the cluster head node, greatly balance the load of network nodes and effectively prolong 15% of the network life time.

The CREW PRAM Complexity of Modular Inversion

One of the long-standing open questions in the theory of parallel computation is the parallel complexity of the integer gcd and related problems, such as modular inversion. We present a lower bound $\Omega (\log n)$ for the parallel time on a concurrent-read exclusive-write parallel random access machine (CREW PRAM) computing the inverse modulo certain n-bit integers, including all such primes. For infinitely many moduli, our lower bound matches asymptotically the known upper bound. We obtain a similar lower bound for computing a specified bit in a large power of an integer. Our main tools are certain estimates for exponential sums in finite fields.

An $\Omega(\sqrt{\,\log\log n}\,)$ Lower Bound for Routing in Optical Networks

Opticalcommunication is likely to significantly speed up parallel computation because the vast bandwidth of the optical medium can be divided to produce communication networks of very high degree. However, the problem of contention in high-degree networks makes the routing problem in these networks theoretically (and practically) difficult. In this paper we examine Valiant's h-relation routing problem, which is a fundamental problem in the theory of parallel computing. The h-relation routing problem arises both in the direct implementation of specific parallel algorithms on distributed-memory machines and in the general simulation of shared-memory models such as the PRAM on distributed-memory machines. In an h-relation routing problem each processor has up to h messages that it wishes to send to other processors and each processor is the destination of at most h messages. We present a lower bound for routing an h-relation (for any h > 1) on a complete optical network of size n. Our lower bound applies to any randomized distributed algorithm for this task. Specifically, we show that the expected number of communication steps required to route an arbitrary h-relation is $\Omega(h + \sqrt{\,\log\log n}\,)$. This is the first known lower bound for this problem which does not restrict the class of algorithms under consideration.

PARADIGMS ADMITTING SUPERUNITARY BEHAVIOUR IN PARALLEL COMPUTATION*

With the expanding role of computers in society, some assumptions underlying well known theorems in the theory of parallel computation no longer hold universally. In particular, the speedup theorem and Brent's theorem do not apply to dynamic computers that interact with their environment. The phenomenon of a disproportionate decrease in execution time of P 2 over p1 processors for p2 > p1 is referred to as superunitary speedup. An analogous phenomenon that we call superunilary 'success ratio’ occurs in dealing with tasks that can either succeed or fail, when there is a disproportionate increase in the success of p2 over p1 processors executing a task. We identify a range of conditions that may lead to superunitary speedup or success ratio, and propose several new paradigms for problems that admit such superunitary behaviour. Our results suggest that a new theory of parallel computation may be required to accommodate these new paradigms.

Cover-preserving order embeddings into Boolean lattices

It is not known which finite graphs occur as induced subgraphs of a hypercube. This is relevant in the theory of parallel computing. The ordered version of the problem is: Which finite posets P occur as cover-preserving subposets of a Boolean lattice? Our main Theorem gives (for 0,1-posets) a necessary and sufficient condition, which involves the chromatic number of a graph associated to P. It is applied respectively to upper balanced, meet extremal, meet semidistributive, and semidistributive lattices P. More specifically, we consider isometric embeddings of posets into Boolean lattices. In particular, answering a question of Ivan Rival to the positive, a nontrivial invariant for the covering graph of a poset is found.

Parallel models of computation: an introductory survey

The paper gives an overview of some models of computation which have proved successful in laying a foundation for a general theory of parallel computation. We present three models of parallel computation, namelyboolean andarithmetic circuit families, andParallel Random Access Machines. They represent different viewpoints on parallel computing: boolean circuit families are useful for in-depth theoretical studies on the power and limitations of parallel computers; Parallel Random Access Machines are the most general vehicles for designing highly parallel algorithms; arithmetic circuit families are an important tool for undertaking studies related to one of the most active areas in parallel computing, i.e. parallel algebraic complexity.

The semantics and complexity of parallel programs for vector computations. Part I: A case study using ADA

Recent research in parallel numerical computation has tended to focus on the algorithmic level. Less attention has been given to the programming level where algorithm is matched, to some extent, to computer architecture. This two-part paper presents a three-level approach to parallel programming which distinguishes between mathematical algorithm, program and computer architecture. In part I, we motivate our approach by a case study using the Ada language. In part II, a mathematical concept of parallel algorithm is introduced in terms of partial orders. This serves as the basis of a theory of parallel computation which makes possible a precise semantics and a precise criterion of complexity of parallel programs. It also suggests some notation for specifying parallel numerical algorithms. To illustrate the ideas presented in part II, we concentrate here on parallel numerical computations which have vector spaces as their central data type and which are intended to be executed on a multi-processor system. The Ada language, with its task constructs, allows one to program computer algorithms to be executed on multi-processor systems, rather than on “vector (pipelined) architectures”. To provide a concrete example of the general problem of programming parallel numerical algorithms for multi-processor computers, we do a case study of how Ada can be used to program the solution of a system of linear equations on such computers. The case study includes an analysis of complexity which addresses the cost of data movement and process control/synchronization as well as the usual arithmetic complexity.