A complexity theory of efficient parallel algorithms

2011 International Conference on Parallel Processing, 2011

For a given algorithm, the energy consumed in executing the algorithm has a nonlinear relationship with performance. In case of parallel algorithms, energy use and performance are functions of the structure of the algorithm. We define the asymptotic energy complexity of algorithms which models the minimum energy required to execute a parallel algorithm for a given execution time as a function of input size. Our methodology provides us with a way of comparing the orders of (minimal) energy required for different algorithms and can be used to define energy complexity classes of parallel algorithms.

2016

In this paper, we provide a qualitative and quantitative analysis of the performance of parallel algorithms on modern multi-core hardware. We attempt to show a comparative study of the performances of algorithms (traditionally perceived as sequential in nature) in a parallel environment, using the Message Passing Interface (MPI) based on Amdahl’s Law. First, we study sorting algorithms. Sorting is a fundamental problem in computer science, and one where there is a limit on the efficiency of algorithms that exist. In theory it contains a large amount of parallelism and should not be difficult to accelerate sorting of very large datasets on modern architectures. Unfortunately, most serial sorting algorithms do not lend themselves to easy parallelization, especially in a distributed memory system such as we might use with MPI. While initial results show a promising speedup for sorting algorithms, owing to inter-process communication latency, we see an slower run-time, overall with incr...

21st Annual Symposium on Foundations of Computer Science (sfcs 1980), 1980

Lecture Notes in Computer Science, 1996

Evaluating how well a whole system or set of subsystems performs is one of the primary objectives of performance testing. We can tell via performance assessment if the architecture implementation meets the design objectives. Performance evaluations of several parallel algorithms are compared in this study. Both theoretical and experimental methods are used in performance assessment as a subdiscipline in computer science. The parallel method outperforms its sequential counterpart in terms of throughput. The parallel algorithm's performance (speedup) is examined, as shown in the result.

Journal of Parallel and Distributed Computing, 1993

There are several metrics that characterize the performance of a parallel system, such as, parallel execution time, speedup and e ciency. A number of properties of these metrics have been studied. For example, it is a well known fact that given a parallel architecture and a problem of a xed size, the speedup of a parallel algorithm does not continue to increase with increasing number of processors. It usually tends to saturate or peak at a certain limit. Thus it may not be useful to employ more than an optimal number of processors for solving a problem on a parallel computer. This optimal number of processors depends on the problem size, the parallel algorithm and the parallel architecture. In this paper we study the impact of parallel processing overheads and the degree of concurrency of a parallel algorithm on the optimal number of processors to be used when the criterion for optimality is minimizing the parallel execution time. We then study a more general criterion of optimality and show how operating at the optimal point is equivalent to operating at a unique value of e ciency which is characteristic of the criterion of optimality and the properties of the parallel system under study. We put the technical results derived in this paper in perspective with similar results that have appeared in the literature before and show how this paper generalizes and/or extends these earlier results.

Lecture Notes in Computer Science, 2002

The emerging discipline of algorithm engineering has primarily focused on transforming pencil-and-paper sequential algorithms into robust, efficient, well tested, and easily used implementations. As parallel computing becomes ubiquitous, we need to extend algorithm engineering techniques to parallel computation. Such an extension adds significant complications. After a short review of algorithm engineering achievements for sequential computing, we review the various complications caused by parallel computing, present some examples of successful efforts, and give a personal view of possible future research.

Springer eBooks, 1991