Parallel Computation Skeletons with Premature Termination Property

Abstract

Abstract. A parallel computation with early termination property is a special form of a parallel for loop. This paper devises a generic highlevel approach for such computation which is expressed as a scheme for algorithmic skeletons. We call this scheme map+reduce, in similarity with the map-reduce paradigm. The implementation is concise and relies heavily on laziness. Two case studies from computational number theory support our presentation.Algorithmic skeletons are parallel algorithm abstractions, which concentrate on the parallelisation and not on the algorithm [1]. We regard here skeletal implementation of a parallel computation with early termination. An imperative equivalent is a for−break parallel loop. An overview is in Section 1. This paper discusses an implementation of this kind of a loop in lazy parallel functional programming language Eden [2]. We will present this language briefly in Section 2. We devise a classification of new and existing related skeletons in Section 3. We develop there a more special approach. The desired parallel behaviour has a wellknown functional counterpart: a map-reduce combination with added possibility of premature termination. This premature abort part is new. We find some features of the Eden language useful in this context, as the premature termination is granted for free in our setting. We discuss it in Section 4. Section 5 highlights two primality tests used as examples. We do not discuss their implementation in full detail and focus on parallelisation results. Section 6 discusses further related work. Section 7 concludes and outlines future work.Contributions. The contributions of this paper are -Definition of the map+reduce skeleton scheme for the parallel computation with premature termination. -Discussion of the importance of laziness in the context of speculative parallelisation and premature termination. -High-level parallelisation of two primality tests. We were the first to parallelise one of them, the Jacobi sum test.

Three Dimensional Reconstruction

“…The remaining 13 videos are found in the repository (doi: 10.5281/zenodo.128861). For each small region, the following processing steps are visualised from left to right in the upper and lower part of the panel: original registered data (1), HSV data conversion (2), HSV data conversion of next serial section (3), interpolations between both serial sections resulting in 7 images (4), final result of all volume filtering operations of interpolated images (5), areas differing between interpolated images and the result of filtering visualised in red colour (6). Video is available under doi: 10.1371/journal.pone.0168173.s021.…”