STORRE Collection: Electronic copies of Computing Science and Mathematics conference papers and proceedings.Electronic copies of Computing Science and Mathematics conference papers and proceedings.http://hdl.handle.net/1893/4782019-09-19T06:22:53Z2019-09-19T06:22:53ZReliable scalable symbolic computation: The design of SymGridPar2Maier, PatrickStewart, RobertTrinder, Phil Whttp://hdl.handle.net/1893/300362019-08-28T12:57:35Z2014-04-01T00:00:00ZTitle: Reliable scalable symbolic computation: The design of SymGridPar2
Author(s): Maier, Patrick; Stewart, Robert; Trinder, Phil W
Abstract: Symbolic computation is an important area of both Mathematics and Computer Science, with many large computations that would benefit from parallel execution. Symbolic computations are, however, challenging to parallelise as they have complex data and control structures, and both dynamic and highly irregular parallelism. The SymGridPar framework (SGP) has been developed to address these challenges on small-scale parallel architectures. However the multicore revolution means that the number of cores and the number of failures are growing exponentially, and that the communication topology is becoming increasingly complex. Hence an improved parallel symbolic computation framework is required. This paper presents the design and initial evaluation of SymGridPar2 (SGP2), a successor to SymGridPar that is designed to provide scalability onto 105 cores, and hence also provide fault tolerance. We present the SGP2 design goals, principles and architecture. We describe how scalability is achieved using layering and by allowing the programmer to control task placement. We outline how fault tolerance is provided by supervising remote computations, and outline higher-level fault tolerance abstractions. We describe the SGP2 implementation status and development plans. We report the scalability and efficiency, including weak scaling to about 32,000 cores, and investigate the overheads of tolerating faults for simple symbolic computations.2014-04-01T00:00:00ZHigh-Performance Computer Algebra: A Hecke Algebra Case StudyMaier, PatrickLivesey, DariaLoidl, Hans-WolfgangTrinder, Philhttp://hdl.handle.net/1893/300352019-08-28T12:56:55Z2014-01-01T00:00:00ZTitle: High-Performance Computer Algebra: A Hecke Algebra Case Study
Author(s): Maier, Patrick; Livesey, Daria; Loidl, Hans-Wolfgang; Trinder, Phil
Editor(s): Silva, F; Dutra, I; Costa Santos, V
Abstract: We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures. Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores.2014-01-01T00:00:00ZThe HdpH DSLs for scalable reliable computationMaier, PatrickStewart, RobertTrinder, Philhttp://hdl.handle.net/1893/300292019-08-28T07:26:28Z2014-09-03T00:00:00ZTitle: The HdpH DSLs for scalable reliable computation
Author(s): Maier, Patrick; Stewart, Robert; Trinder, Phil
Abstract: The statelessness of functional computations facilitates both parallelism and fault recovery. Faults and non-uniform communication topologies are key challenges for emergent large scale parallel architectures. We report on HdpH and HdpH-RS, a pair of Haskell DSLs designed to address these challenges for irregular task-parallel computations on large distributed-memory architectures. Both DSLs share an API combining explicit task placement with sophisticated work stealing. HdpH focuses on scalability by making placement and stealing topology aware whereas HdpH-RS delivers reliability by means of fault tolerant work stealing. We present operational semantics for both DSLs and investigate conditions for semantic equivalence of HdpH and HdpH-RS programs, that is, conditions under which topology awareness can be transparently traded for fault tolerance. We detail how the DSL implementations realise topology awareness and fault tolerance. We report an initial evaluation of scalability and fault tolerance on a 256-core cluster and on up to 32K cores of an HPC platform.2014-09-03T00:00:00ZQuery Filtering with Low-Dimensional Local EmbeddingsChávez, EdgarConnor, RichardVadicamo, Luciahttp://hdl.handle.net/1893/300242019-08-23T10:00:24ZTitle: Query Filtering with Low-Dimensional Local Embeddings
Author(s): Chávez, Edgar; Connor, Richard; Vadicamo, Lucia
Abstract: The concept of local pivoting is to partition a metric space so that each element in the space is associated with precisely one of a fixed set of reference objects or pivots. The idea is that each object of the data set is associated with the reference object that is best suited to filter that particular object if it is not relevant to a query, maximising the probability of excluding it from a search. The notion does not in itself lead to a scalable search mechanism, but instead gives a good chance of exclusion based on a tiny memory footprint and a fast calculation. It is therefore most useful in contexts where main memory is at a premium, or in conjunction with another, scalable, mechanism. In this paper we apply similar reasoning to metric spaces which possess the four-point property, which notably include Euclidean, Cosine, Triangular, Jensen-Shannon, and Quadratic Form. In this case, each element of the space can be associated with two reference objects, and a four-point lower-bound property is used instead of the simple triangle inequality. The probability of exclusion is strictly greater than with simple local pivoting; the space required per object and the calculation are again tiny in relative terms. We show that the resulting mechanism can be very effective. A consequence of using the four-point property is that, for m reference points, there arèarè m 2 ´ pivot pairs to choose from, giving a very good chance of a good selection being available from a small number of distance calculations. Finding the best pair has a quadratic cost with the number of references ; however, we provide experimental evidence that good heuristics exist. Finally, we show how the resulting mechanism can be integrated with a more scalable technique to provide a very significant performance improvement, for a very small overhead in build-time and memory cost. Keywords: metric search · extreme pivoting · supermetric space · four-point property · pivot based index 2 Chávez et al.