Grid computing provides a powerful, virtual parallel system known as a computational Grid on which users can run parallel applications to solve problems quickly. However, users must be careful to allocate tasks to nodes properly because improper allocation of only one task could result in lengthy executions of applications, or even worse, applications could crash. This allocation problem is called the mapping problem, and an entity that tackles this problem is called a mapper. In this thesis, we aim to develop an efficient, practical, portable mapper. To study the mapping problem, researchers often make unrealistic assumptions such as that nodes of Grids are always reliable, that execution times of tasks assigned to nodes are known a priori, or that detailed information of parallel applications is always known. As a result, the practicality and portability of mappers developed in such conditions are uncertain. Our review of related work suggested that a more efficient tool is required to study this problem; therefore, we developed GMap, a simulator researchers/developers can use to develop practical, portable mappers. The fact that nodes are not always reliable leads to the development of an algorithm for predicting the reliability of nodes and a predictor for identifying reliable nodes of Grids. Experimental results showed that the predictor reduced the chance of failures in executions of applications by half. The facts that execution times of tasks assigned to nodes are not known a priori and that detailed information of parallel applications is not alw ays known, lead to the evaluation of five nearest-neighbour (nn) execution time estimators: k-nn smoothing, k-nn, adaptive k-nn, one-nn, and adaptive one-nn. Experimental results showed that adaptive k-nn was the most efficient one. We also implemented the predictor and the estimator in GMap. Using GMap, we could reliably compare the efficiency of six mapping algorithms: Min-min, Max-min, Genetic Algorithms, Simulated Annealing, Tabu Search, and Quick-quality Map, with none of the preceding unrealistic assumptions. Experimental results showed that Quick-quality Map was the most efficient one. As a result of these findings, we achieved our goal in developing an efficient, practical, portable mapper.

Thesis--Universität Erlangen-Nürnberg, 1994.

The Message Passing Interface (MPI) standard defines virtual topologies that can be applied to systems of cooperating processes. Among issues regarding a more convenient namespace this may be used to optimize the placement of MPI processes in order to reduce communication time. That means, the processes with their main communication paths represent a graph that has to be cost efficiently mapped onto the graph representing the actual communication network. In this context, this work analyses and compares state-of-the-art task mapping strategies with respect to running time and their quality of solutions to the MPI mapping problem. In particular, the focus is on generic strategies that can be used for arbitrary process/network topologies although, here, the topologies of interest are regular ones, where the number of processes is greater than the number of processors in the underlying physical network. Additionally, different measures of mapping quality are discussed and a close correspondence between the most appropriate, the weighted edge cut, and program execution time is shown. In order to investigate how mapping quality affects MPI program execution time, some mapping strategies have been incorporated into Open MPI. Finally, benchmark results prove that optimized process-to-processor mappings can improve program execution time by up to 60%, compared to the default mapping in many MPI implementations (linear mapping). The findings in this work can serve as reference not only for MPI implementors, but also for researchers investigating static process-to-processor mappings, in general.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.44-49).

The Message Passing Interface (MPI) standard defines virtual topologies that can be applied to systems of cooperating processes. Among issues regarding a more convenient namespace this may be used to optimize the placement of MPI processes in order to reduce communication time. That means, the processes with their main communication paths represent a graph that has to be cost efficiently mapped onto the graph representing the actual communication network. In this context, this work analyses and compares state-of-the-art task mapping strategies with respect to running time and their quality of solutions to the MPI mapping problem. In particular, the focus is on generic strategies that can be used for arbitrary process/network topologies although, here, the topologies of interest are regular ones, where the number of processes is greater than the number of processors in the underlying physical network. Additionally, different measures of mapping quality are discussed and a close correspondence between the most appropriate, the weighted edge cut, and program execution time is shown. In order to investigate how mapping quality affects MPI program execution time, some mapping strategies have been incorporated into Open MPI. Finally, benchmark results prove that optimized process-to-processor mappings can improve program execution time by up to 60%, compared to the default mapping in many MPI implementations (linear mapping). The findings in this work can serve as reference not only for MPI implementors, but also for researchers investigating static process-to-processor mappings, in general.

Monte Carlo simulations are embarrassingly parallel in nature, so having a parallel and efficient random number generator becomes crucial. To have a parallel generator with uncorrelated processors, parallelization methods are implemented together with a binary tree mapping. Although, this method has considerable advantages, because of the constraints arising from the binary tree structure, a situation defined as problem of falling off the tree occurs. In this thesis, a new spawning method that is based on binary tree traversal and new spawn processor appointment is proposed to use when falling off the tree problem is encountered. With this method, it is seen that, spawning operation becomes more costly but the independency of parallel processors is guaranteed. In Monte Carlo simulations, random number generation time should be unperceivable when compared with the execution time of the whole simulation. That is why / linear congruential generators with Mersenne prime moduli are used. In highly branching Monte Carlo simulations, cost of parameterization also gains importance and it becomes reasonable to consider other types of primes or other parallelization methods that provide different balance between parameterization cost and random number generation cost. With this idea in mind, in this thesis, for improving performance of linear congruential generators, two approaches are proposed. First one is using Sophie-Germain primes as moduli and second one is using a hybrid method combining both parameterization and splitting techniques. Performance consequences of Sophie-Germain primes over Mersenne primes are shown through graphics. It is observed that for some cases proposed approaches have better performance consequences.