Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

Algorithms for hierarchical and semi-partitioned parallel scheduling

International audienceWe propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such asunrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem andleverage its fractional relaxation to obtain a polynomial-time 2- approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

Hierarchical Scheduling for Real-Time Periodic Tasks in Symmetric Multiprocessing

In this paper, we present a new hierarchical scheduling framework for periodic tasks in symmetric multiprocessor (SMP) platforms. Partitioned and global scheduling are the two main approaches used by SMP based systems where global scheduling is recommended for overall performance and partitioned scheduling is recommended for hard real-time performance. Our approach combines both the global and partitioned approaches of traditional SMP-based schedulers to provide hard real-time performance guarantees for critical tasks and improved response times for soft real-time tasks. Implemented as part of VxWorks, the results are confirmed using a real-time benchmark application, where response times were improved for soft real-time tasks while still providing hard real-time performance

An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK -- STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices