Parallelism with limited nondeterminism

Computational complexity theory studies which computational problems can be solved with limited access to resources. The past fifty years have seen a focus on the relationship between intractable problems and efficient algorithms. However, the relationship between inherently sequential problems and highly parallel algorithms has not been as well studied. Are there efficient but inherently sequential problems that admit some relaxed form of highly parallel algorithm? In this dissertation, we develop the theory of structural complexity around this relationship for three common types of computational problems. Specifically, we show tradeoffs between time, nondeterminism, and parallelizability. By clearly defining the notions and complexity classes that capture our intuition for parallelizable and sequential problems, we create a comprehensive framework for rigorously proving parallelizability and non-parallelizability of computational problems. This framework provides the means to prove whether otherwise tractable problems can be effectively parallelized, a need highlighted by the current growth of multiprocessor systems. The views adopted by this dissertation—alternate approaches to solving sequential problems using approximation, limited nondeterminism, and parameterization—can be applied practically throughout computer science

Designing Efficient Parallel Algorithms for Graph Problems

Graph algorithms are concerned with the algorithmic aspects of solving graph problems. The problems are motivated from and have application to diverse areas of computer science, engineering and other disciplines. Problems arising from these areas of application are good candidates for parallelization since they often have both intense computational needs and stringent response time requirements. Motivated by these concerns, this thesis investigates parallel algorithms for these kinds of graph problems that have at least one of the following properties: the problems involve some type of dynamic updates; the sparsification technique is applicable; or the problems are closely related to communications network issues. The models of parallel computation used in our studies are the Parallel Random Access Machine (PRAM) model and the practical interconnection network models such as meshes and hypercubes. ¶ ..

Distributed Parallel Computing for Visual Cryptography Algorithms

Proceedings of: Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015). Krakow (Poland), September 10-11, 2015.The recent activities to construct exascale and ultrascale distributed computational systems are opening a possibility to apply parallel and distributed computing techniques for applied problems which previously were considered as not solvable with the standard computational resources. In this paper we consider one global optimization problem where a set of feasible solutions is discrete and very large. There is no possibility to apply some apriori estimation techniques to exclude an essential part of these elements from the computational analysis, e.g. applying branch and bound type methods. Thus a full search is required in order to solve such global optimization problems. The considered problem describes visual cryptography algorithms. The main goal is to find optimal perfect gratings, which can guarantee high quality and security of the visual cryptography method. The full search parallel algorithm is based on master-slave paradigm. We present a library of C++ templates that allow the developer to implement parallel master-slave algorithms for his application without any parallel programming and knowledge of parallel programming API. These templates automatically give parallel solvers tailored for clusters of computers using MPI API and distributed computing applications using BOINC API. Results of some computational experiments are presented.The work presented in this paper has been partially supported by EU under the COST programme Action IC1305, ’Network for Sustainable Ultrascale Computing (NESUS)’

Definition of a Method for the Formulation of Problems to be Solved with High Performance Computing

Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of parallel computing such as message passing and shared memory. Few case studies are considered to show when the shared memory model is suitable and when the message passing model would be suitable. The models of parallel computing are implemented and evaluated using some algorithms and simulations. This thesis mainly focuses on showing the more suitable model of computing for the various scenarios in attaining High Performance Computing

Experiments with parallel algorithms for combinatorial problems

In the last decade many models for parallel computation have been proposed and many parallel algorithms have been developed. However, few of these models have been realized and most of these algorithms are supposed to run on idealized, unrealistic parallel machines. The parallel machines constructed so far all use a simple model of parallel computation. Therefore, not every existing parallel machine is equally well suited for each type of algorithm. The adaptation of a certain algorithm to a specific parallel archi- tecture may severely increase the complexity of the algorithm or severely obscure its essence. Little is known about the performance of some standard combinatorial algorithms on existing parallel machines. In this paper we present computational results concerning the solution of knapsack, shortest paths and change-making problems by branch and bound, dynamic programming, and divide and conquer algorithms on the ICL-DAP (an SIMD computer), the Manchester dataflow machine and the CDC-CYBER-205 (a pipeline computer)

Development of Parallel Algorithms for Computer Vision

Computer vision is an important research area where computationally-intensive and time critical problems need to be solved routinely. This paper described some parallel algorithms for image processing and computational geometry applicable to the field of 'robot vision' which was developed using PACE parallel computer, a closely coupled message passing MIMD machine, designed and developed at the Advanced Numerical Reserach & Analysis Group, Hyderabad

Tight bounds for some problems in computational geometry: the complete sub-logarithmic parallel time range

There are a number of fundamental problems in computational geometry for which work-optimal algorithms exist which have a parallel running time of $O(\log n)$ in the PRAM model. These include problems like two and three dimensional convex-hulls, trapezoidal decomposition, arrangement construction, dominance among others. Further improvements in running time to sub-logarithmic range were not considered likely because of their close relationship to sorting for which an $\Omega (\log n/\log\log n )$ is known to hold even with a polynomial number of processors. However, with recent progress in padded-sort algorithms, which circumvents the conventional lower-bounds, there arises a natural question about speeding up algorithms for the above-mentioned geometric problems (with appropriate modifications in the output specification). We present randomized parallel algorithms for some fundamental problems like convex-hulls and trapezoidal decomposition which execute in time $O( \log n/\log k)$ in an $nk$ ($k > 1$) processor CRCW PRAM. Our algorithms do not make any assumptions about the input distribution. Our work relies heavily on results on padded-sorting and some earlier results of Reif and Sen [28, 27]. We further prove a matching lower-bound for these problems in the bounded degree decision tree