Maximize subject to 1) 2) 3)

1. Round of data installments (time length = R) L Communications over the network C Receive (red) and compute operation sequences MT A User-level Scheduler for the Execution of Master-worker Divisible Tasks on Homogeneuous Clusters Luis de la torre-quintana Torre_dl@math.uprm.edu Advisor: Jaime Seguel, PHd UNIVERSITY OF Puerto Rico at Mayagüez Computer and electrical engineering INTRODUCTION Multiround periodic schedule Case studies Load-and task-divisible jobs consist of a core task that is repeated a number of times over different data chunks. In single-program multiple-data style (SPMD), these jobs are implemented as nested sequences of do-loops around the core task. Usually, a master process distributes data chunks across all participating workers in what is often called a round of data installments. Each data installment is followed by a receive and a compute operation, both performed by the receiving worker. Workers receive and compute their core tasks concurrently. In SPMD implementations rounds are controlled by an external do-loop, which imposes the periodic character of the job's execution. The main parameters in a SPMD implementation are thus, the number of rounds, denoted below by nRound, and the number of workers involved in the concurrent computations, denoted below by nWorkers. Master Comparison with Uniform Multiround Algo- rithm(UMR) Link Worker 1 Worker 2 Worker 3 Worker 4 UMR[1] is a multiround algorithm for scheduling divisible loads on parallel computing systems. The next table shows comparisons of UMR performance and our scheduler for a load of 1000 core jobs under different bandwidths. Worker 5 5 workers, 6 periods and an additional round SCHEME General concept of period Maximal production problem Without agglomeration of core tasks For j = 1, nRounds If Master process For i = 1, nWorkers “Retrieve data chunk for worker i” “Send data chunk to worker i” Else “Receive agglomerated data chunk” “Compute core task on data chunk” Agglomeration of core tasks For j = 1, nRounds If Master process For i = 1, nWorkers “Retrieve agglomerated data chunks for worker i” “Send agglomerated data chunk to worker i” Else “Receive agglomerated data chunk” For j = 1, nCoreTasks “Compute core task” An improved parallel motif finding solver (PMFS) Maximize subject to 1) 2) 3) Given a set of t DNA sequences, the motif finding problem consists in finding a set of t strings with l characters; one from each sequence, that maximizes the consensus score. Next we compare a PMFS scheduled with FIFO versus our scheduler. Theorem 1: Let T and X be a real nonnegative numbers and k be a positive integer. Let Y = (r + w)-1(T) them MMP-MP 420 agglomerated tasks Minimal makespan problem (MMP-MP) FUTURE WORK Problem scenario The problem of minimizing the makespan under maximal production constrains is stated as: This work will be extended to heterogeneous parallel computing platforms Minimize(T) = (v+1/2)T + (e + g + r + w)(Y ) subject to 1) Y = (r + w)-1(T) 2) 3) 4) ACKNOWLEDGEMENTS This work was supported in part by a CISE fellowship grant, and NIH-MARC grant Parallel computing platforms Computer programmer REFERENCES Concurrent (task) load distribution Theorem 2: Let X be a nonnegative real number and i the number of processors. Then the solution to problem without restriction 4, Serial processing • Y. Yang, K. van der Raadt, H. Casanove, Multiround Algorithms for Scheduling Divisible Loads, IEEE Transactions on Parallel and Distributed Systems, Vol. 16, No. 11, 2005 • C. Banino, O. Beaumont, L. Carter, J. Ferrante, A. Legrand and Y. Robert, Scheduling Strategies for Master-slave Tasking on Heterogeneous Processor Platforms, IEEE Transactions on Parallel and Distributed Systems,Vol. 15, No. 4, pp. 319-330, 2004 • M. Drozdowski and P. Wolniewicz Optimum Divisible Load Scheduling on Heterogeneous Stars with Limited Memory, European Journal of Operation Research, Vol. 172, No. 2, 2006. • N. Jones and P. Pevzner An Introduction to Bioinformatics Algorithms, MIT Press, 2000. Concurrent task processing Platform Model MMP-MP is reduced to finding the minimal value of (T) with i ranging over the subset the i that satisfying CISE POSTER PRESENTATION OCTOBER 21ST 2008