Multiprocessing the Sieve of Eratosthenes

The Sieve of Eratosthenes for finding prime numbers in recent years has seen much use as a benchmark algorithm for serial computers while its intrinsically parallel nature has gone largely unnoticed. The implementation of a parallel version of this algorithm for a real parallel computer, the Flex/32, is described and its performance discussed. It is shown that the algorithm is sensitive to several fundamental performance parameters of parallel machines, such as spawning time, signaling time, memory access, and overhead of process switching. Because of the nature of the algorithm, it is impossible to get any speedup beyond 4 or 5 processors unless some form of dynamic load balancing is employed. We describe the performance of our algorithm with and without load balancing and compare it with theoretical lower bounds and simulated results. It is straightforward to understand this algorithm and to check the final results. However, its efficient implementation on a real parallel machine requires thoughtful design, especially if dynamic load balancing is desired. The fundamental operations required by the algorithm are very simple: this means that the slightest overhead appears prominently in performance data. The Sieve thus serves not only as a very severe test of the capabilities of a parallel processor but is also an interesting challenge for the programmer

Memory Efficient Multithreaded Incremental Segmented Sieve Algorithm

Prime numbers are fundamental in number theory and play a significant role in various areas, from pure mathematics to practical applications, including cryptography. In this contribution, we introduce a multithreaded implementation of the Segmented Sieve algorithm. In our implementation, instead of handling large prime ranges in one iteration, the sieving process is broken down incrementally, which theoretically eliminates the challenges of working with large numbers, and can reduce memory usage, providing overall more efficient multi-core utilization over extended computations.Comment: 10 page

Towards Type-Based Optimizations in Distributed Applications Using ABS and JAVA 8

In this paper we present an API to support modeling applications with Actors based on the paradigm of the Abstract Behavioural Specification (ABS) language. With the introduction of JAVA 8, we expose this API through a JAVA library to allow for a high-level actor-based methodology for programming distributed systems which supports the programming to interfaces discipline. We validate this solution through a case study where we obtain significant performance improvements as well as illustrating the ease with which simple high and low-level optimizations can be obtained by examining topologies and communication within an application. Using this API we show it is much easier to observe drawbacks of shared data-structures and communications methods in the design phase of a distributed application and apply the necessary corrections in order to obtain better results

A distributed prime sieving algorithm based on SMER

Rapport interne LIPNIn this paper, we propose a fully distributed algorithm for finding all primes in an given interval $[2..n]$ (or $(L,R)$, more generally), based on the SMER (\textit{Scheduling by Multiple Edge Reversal}) multigraph dynamics. Given a multigraph $\mathcal{M}$ of arbitrary topology, having $N$ nodes, the SMER-driven system is defined by the numberof directed edges (arcs) between any two nodes of $\mathcal{M}$, and by the global period length of all ``arc reversals'' in $\mathcal{M}$. In the domain of prime numbers generation, such a graph method shows quite elegant, and it also yields a totally new kind of distributed prime sieving algorithms of an entirely original design. The maximum number of steps required by the algorithm is at most $n + \sqrt{n}$. Although far beyond the $O(n/\log\log n)$ steps required by the improved sequential ``wheel sieve'' algorithms, our SMER-based algorithm is fully distributed and of linear (step) complexity. The message complexity of the algorithm is at most $n\Delta_N + \sqrt{n} \Delta_N$, where $\Delta_N$ denotes the maximum ``multidegree'' of the arbitrary multigraph $\mathcal{M}$, and the space required per process is linear

A distributed wheel sieve algorithm using Scheduling by Multiple Edge Reversal

Number of pages: 12This paper presents a new distributed approach for generating all prime numbers in a given interval of integers. From Eratosthenes, who elaborated the first prime sieve (more than 2000 years ago), to the current generation of parallel computers, which have permitted to reach larger bounds on the interval or to obtain previous results in a shorter time, prime numbers generation still represents an attractive domain of research and plays a central role in cryptography. We propose a fully distributed algorithm for finding all primes in the interval $[2\ldots, n]$, based on the \emph{wheel sieve} and the SMER (\emph{Scheduling by Multiple Edge Reversal}) multigraph dynamics. Given a multigraph $\mathcal{M}$ of arbitrary topology, having $N$ nodes, an SMER-driven system is defined by the number of directed edges (arcs) between any two nodes of $\mathcal{M}$, and by the global period length of all ''arc reversals'' in $\mathcal{M}$. The new prime number generation method inherits the distributed and parallel nature of SMER and requires at most $n + \lfloor \sqrt{n}\rfloor$ time steps

A design pattern for optimizations in data intensive applications using ABS and JAVA 8

Cloud environments have become a standard method for enterprises to offer their applications by means of web services, data management systems, or simply renting out computing resources. In our previous work, we presented how we can use a modeling language together with the new features of JAVA 8 to overcome certain drawbacks of data structures and synchronization mechanisms in parallel applications. We extend this solution into a design pattern that allows application-specific optimizations in a distributed setting. We validate this integration using our previous case study of the Prime Sieve of Eratosthenes and illustrate the performance improvements in terms of speed-up and memory co

A design pattern for optimizations in data intensive applications using ABS and JAVA 8

Cloud environments have become a standard method for enterprises to offer their applications by means of web services, data management systems, or simply renting out computing resources. In our previous work, we presented how we can use a modeling language together with the new features of JAVA 8 to overcome certain drawbacks of data structures and synchronization mechanisms in parallel applications. We extend this solution into a design pattern that allows application-specific optimizations in a distributed setting. We validate this integration using our previous case study of the Prime Sieve of Eratosthenes and illustrate the performance improvements in terms of speed-up and memory consumption

A study of real-time operating systems for microcomputers

This thesis describes the evaluation of four operating systems for microcomputers. The emphasis of the study is on the suitability of the operating systems for use in real-time applications, such as process control. The evaluation was performed in two sections. The first section was a quantitative assessment of the performance of the real-time features of the operating system. This was performed using benchmarks. The criteria for the benchmarks and their design are discussed. The second section was a qualitative assessment of the suitability of the operating systems for the development and implementation of real-time systems. This was assessed through the implementation of a small simulation of a manufacturing process and its associated control system. The simulation was designed using the Ward and Mellor real-time design method which was extended to handle the special case of a real-time simulation. The operating systems which were selected for the study covered a spectrum from general purpose operating systems to small, specialised real-time operating systems. From the quantitative assessment it emerged that QNX (from Quantum Software Systems) had the best overall performance. Qualitatively, UNIX was found to offer the best system development environment, but it does not have the performance and the characteristics required for real-time applications. This suggests that versions of UNIX that are adapted for real-time applications are worth careful consideration for use both as development systems and implementation systems