Hybrid static/dynamic scheduling for already optimized dense matrix factorization

We present the use of a hybrid static/dynamic scheduling strategy of the task dependency graph for direct methods used in dense numerical linear algebra. This strategy provides a balance of data locality, load balance, and low dequeue overhead. We show that the usage of this scheduling in communication avoiding dense factorization leads to significant performance gains. On a 48 core AMD Opteron NUMA machine, our experiments show that we can achieve up to 64% improvement over a version of CALU that uses fully dynamic scheduling, and up to 30% improvement over the version of CALU that uses fully static scheduling. On a 16-core Intel Xeon machine, our hybrid static/dynamic scheduling approach is up to 8% faster than the version of CALU that uses a fully static scheduling or fully dynamic scheduling. Our algorithm leads to speedups over the corresponding routines for computing LU factorization in well known libraries. On the 48 core AMD NUMA machine, our best implementation is up to 110% faster than MKL, while on the 16 core Intel Xeon machine, it is up to 82% faster than MKL. Our approach also shows significant speedups compared with PLASMA on both of these systems

Scheduling MapReduce Jobs under Multi-Round Precedences

We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on identical and unrelated parallel processors. For identical processors, we present LP-based O(1)-approximation algorithms. For unrelated processors, the approximation ratio naturally depends on the maximum number of rounds of any job. Since the number of rounds per job in typical MapReduce algorithms is a small constant, our scheduling algorithms achieve a small approximation ratio in practice. For the single-round case, we substantially improve on previously best known approximation guarantees for both identical and unrelated processors. Moreover, we conduct an experimental analysis and compare the performance of our algorithms against a fast heuristic and a lower bound on the optimal solution, thus demonstrating their promising practical performance

Policy-based techniques for self-managing parallel applications

This paper presents an empirical investigation of policy-based self-management techniques for parallel applications executing in loosely-coupled environments. The dynamic and heterogeneous nature of these environments is discussed and the special considerations for parallel applications are identified. An adaptive strategy for the run-time deployment of tasks of parallel applications is presented. The strategy is based on embedding numerous policies which are informed by contextual and environmental inputs. The policies govern various aspects of behaviour, enhancing flexibility so that the goals of efficiency and performance are achieved despite high levels of environmental variability. A prototype self-managing parallel application is used as a vehicle to explore the feasibility and benefits of the strategy. In particular, several aspects of stability are investigated. The implementation and behaviour of three policies are discussed and sample results examined

Extending the Nested Parallel Model to the Nested Dataflow Model with Provably Efficient Schedulers

The nested parallel (a.k.a. fork-join) model is widely used for writing parallel programs. However, the two composition constructs, i.e. "$\parallel$" (parallel) and "$;$" (serial), are insufficient in expressing "partial dependencies" or "partial parallelism" in a program. We propose a new dataflow composition construct "$\leadsto$" to express partial dependencies in algorithms in a processor- and cache-oblivious way, thus extending the Nested Parallel (NP) model to the \emph{Nested Dataflow} (ND) model. We redesign several divide-and-conquer algorithms ranging from dense linear algebra to dynamic-programming in the ND model and prove that they all have optimal span while retaining optimal cache complexity. We propose the design of runtime schedulers that map ND programs to multicore processors with multiple levels of possibly shared caches (i.e, Parallel Memory Hierarchies) and provide theoretical guarantees on their ability to preserve locality and load balance. For this, we adapt space-bounded (SB) schedulers for the ND model. We show that our algorithms have increased "parallelizability" in the ND model, and that SB schedulers can use the extra parallelizability to achieve asymptotically optimal bounds on cache misses and running time on a greater number of processors than in the NP model. The running time for the algorithms in this paper is $O\left(\frac{\sum_{i=0}^{h-1} Q^{*}({\mathsf t};\sigma\cdot M_i)\cdot C_i}{p}\right)$, where $Q^{*}$ is the cache complexity of task ${\mathsf t}$, $C_i$ is the cost of cache miss at level-$i$ cache which is of size $M_i$, $\sigma\in(0,1)$ is a constant, and $p$ is the number of processors in an $h$-level cache hierarchy