Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
LogP: towards a realistic model of parallel computation
PPOPP '93 Proceedings of the fourth ACM SIGPLAN symposium on Principles and practice of parallel programming
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
An approximation scheme for strip packing of rectangles with bounded dimensions
Discrete Applied Mathematics
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Scheduling Algorithms
Parallel Real Root Isolation Using the Descartes Method
HiPC '99 Proceedings of the 6th International Conference on High Performance Computing
Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial-Time Approximation Scheme
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Scheduling parallel eigenvalue computations in a quantum chemistry code
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
Optimized composition of performance-aware parallel components
Concurrency and Computation: Practice & Experience
A(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
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We consider the problem of finding a schedule for n-independent identical malleable tasks on p identical processors with minimal completion time. This problem arises while using the branch-and-bound or the divide-and-conquer strategy to solve a problem on a parallel system. If nothing is known about the subproblems, then they are assumed to be identical. We assume that the execution time decreases with the number of processors while the computational work increases. We give an algorithm with execution time exponential in p which computes an optimal schedule. In order to approximate an optimal schedule, we use the concept of phase-by-phase schedules. Here schedules consist of phases in which every job uses the same number of processors. We prove that one can approximate an optimal schedule up to a factor of 5/4 using constant time, and we show that this is optimal. Furthermore, we give an ε-approximation algorithm if the speed-up is optimal up to a constant factor.