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Register a new userA Note on Parallel Algorithmic Speedup Bounds
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Added by
Neil J. Gunther
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Authors
Neil J. Gunther
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A parallel program can be represented as a directed acyclic graph. An important performance bound is the time to execute the critical path through the graph. We show how this performance metric is related to Amdahl speedup and the degree of average parallelism. These bounds formally exclude superlinear performance.
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We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, such as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually increasing its makespan (execution time). The slowdown ratio describes how additional constraints affect the makespan. We disprove an existing conjecture positing a bound of two on the slowdown when workload is not considered. Where workload is known, we conjecture that 4/3 slowdown is always achievable, and prove our conjecture for small networks using max-plus algebra. We analyse a polynomial-time algorithm showing that achieving 4/3 slowdown is in exp-APX. Finally, we discuss the implications of our results.
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Due to the increasing size of HPC machines, the fault presence is becoming an eventuality that applications must face. Natively, MPI provides no support for the execution past the detection of a fault, and this is becoming more and more constraining. With the introduction of ULFM (User Level Fault Mitigation library), it has been provided with a possible way to overtake a fault during the application execution at the cost of code modifications. ULFM is intrusive in the application and requires also a deep understanding of its recovery procedures. In this paper we propose Legio, a framework that lowers the complexity of introducing resiliency in an embarrassingly parallel MPI application. By hiding ULFM behind the MPI calls, the library is capable to expose resiliency features to the application in a transparent manner thus removing any integration effort. Upon fault, the failed nodes are discarded and the execution continues only with the non-failed ones. A hierarchical implementation of the solution has been also proposed to reduce the overhead of the repair process when scaling towards a large number of nodes. We evaluated our solutions on the Marconi100 cluster at CINECA, showing that the overhead introduced by the library is negligible and it does not limit the scalability properties of MPI. Moreover, we also integrated the solution in real-world applications to further prove its robustness by injecting faults.
The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors. Performance of many scientific applications such as Molecular Dynamic simulations depends on the underlying 3D parallel FFT library being used. In this paper, we present C-DACs three-dimensional Fast Fourier Transform (CROFT) library which implements three-dimensional parallel FFT using pencil decomposition. To exploit the hyperthreading capabilities of processor cores without affecting performance, CROFT is designed to use multithreading along with MPI. CROFT implementation has an innovative feature of overlapping compute and memory-I/O with MPI communication using multithreading. As opposed to other 3D FFT implementations, CROFT uses only two threads where one thread is dedicated for communication so that it can be effectively overlapped with computations. Thus, depending on the number of processes used, CROFT achieves performance improvement of about 51% to 42% as compared to FFTW3 library.
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