Malleable task-graph scheduling with a practical speed-up model

Scientific workloads are often described by Directed Acyclic task Graphs.Indeed, DAGs represent both a model frequently studied in theoretical literature and the structure employed by dynamic runtime schedulers to handle HPC applications. A natural problem is then to compute a makespan-minimizing schedule of a given graph. In this paper, we are motivated by task graphs arising from multifrontal factorizations of sparsematrices and therefore work under the following practical model. We focus on malleable tasks (i.e., a single task can be allotted a time-varying number of processors) and specifically on a simple yet realistic speedup model: each task can be perfectly parallelized, but only up to a limited number of processors. We first prove that the associated decision problem of minimizing the makespan is NP-Complete. Then, we study a widely used algorithm, PropScheduling, under this practical model and propose a new strategy GreedyFilling. Even though both strategies are 2-approximations, experiments on real and synthetic data sets show that GreedyFilling achieves significantly lower makespans

Task scheduling for parallel multifrontal methods

Abstract. We present a new scheduling algorithm for task graphs arising from parallel multifrontal methods for sparse linear systems. This algorithm is based on the theorem proved by Prasanna and Musicus [1] for tree-shaped task graphs, when all tasks exhibit the same degree of parallelism. We propose extended versions of this algorithm to take communication between tasks and memory balancing into account. The efficiency of proposed approach is assessed by a set of experiments on a set of large sparse matrices from several libraries

Algorithmic Graph Theory

The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions

Theory and Engineering of Scheduling Parallel Jobs

Scheduling is very important for an efficient utilization of modern parallel computing systems. In this thesis, four main research areas for scheduling are investigated: the interplay and distribution of decision makers, the efficient schedule computation, efficient scheduling for the memory hierarchy and energy-efficiency. The main result is a provably fast and efficient scheduling algorithm for malleable jobs. Experiments show the importance and possibilities of scheduling considering the memory hierarchy

Resiliency in numerical algorithm design for extreme scale simulations

This work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 1023 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.Peer Reviewed"Article signat per 36 autors/es: Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt, Leonardo Bautista-Gomez, Tommaso Benacchio, Luca Bonaventura, Hans-Joachim Bungartz, Sanjay Chatterjee, Florina M. Ciorba, Nathan DeBardeleben, Daniel Drzisga, Sebastian Eibl, Christian Engelmann, Wilfried N. Gansterer, Luc Giraud, Dominik G ̈oddeke, Marco Heisig, Fabienne Jezequel, Nils Kohl, Xiaoye Sherry Li, Romain Lion, Miriam Mehl, Paul Mycek, Michael Obersteiner, Enrique S. Quintana-Ortiz, Francesco Rizzi, Ulrich Rude, Martin Schulz, Fred Fung, Robert Speck, Linda Stals, Keita Teranishi, Samuel Thibault, Dominik Thonnes, Andreas Wagner and Barbara Wohlmuth"Postprint (author's final draft

Methodology for malleable applications on distributed memory systems

A la portada logo BSC(English) The dominant programming approach for scientific and industrial computing on clusters is MPI+X. While there are a variety of approaches within the node, denoted by the ``X'', Message Passing interface (MPI) is the standard for programming multiple nodes with distributed memory. This thesis argues that the OmpSs-2 tasking model can be extended beyond the node to naturally support distributed memory, with three benefits: First, at small to medium scale the tasking model is a simpler and more productive alternative to MPI. It eliminates the need to distribute the data explicitly and convert all dependencies into explicit message passing. It also avoids the complexity of hybrid programming using MPI+X. Second, the ability to offload parts of the computation among the nodes enables the runtime to automatically balance the loads in a full-scale MPI+X program. This approach does not require a cost model, and it is able to transparently balance the computational loads across the whole program, on all its nodes. Third, because the runtime handles all low-level aspects of data distribution and communication, it can change the resource allocation dynamically, in a way that is transparent to the application. This thesis describes the design, development and evaluation of OmpSs-2@Cluster, a programming model and runtime system that extends the OmpSs-2 model to allow a virtually unmodified OmpSs-2 program to run across multiple distributed memory nodes. For well-balanced applications it provides similar performance to MPI+OpenMP on up to 16 nodes, and it improves performance by up to 2x for irregular and unbalanced applications like Cholesky factorization. This work also extended OmpSs-2@Cluster for interoperability with MPI and Barcelona Supercomputing Center (BSC)'s state-of-the-art Dynamic Load Balance (DLB) library in order to dynamically balance MPI+OmpSs-2 applications by transparently offloading tasks among nodes. This approach reduces the execution time of a microscale solid mechanics application by 46% on 64 nodes and on a synthetic benchmark, it is within 10% of perfect load balancing on up to 8 nodes. Finally, the runtime was extended to transparently support malleability for pure OmpSs-2@Cluster programs and interoperate with the Resources Management System (RMS). The only change to the application is to explicitly call an API function to control the addition or removal of nodes. In this regard we additionally provide the runtime with the ability to semi-transparently save and recover part of the application status to perform checkpoint and restart. Such a feature hides the complexity of data redistribution and parallel IO from the user while allowing the program to recover and continue previous executions. Our work is a starting point for future research on fault tolerance. In summary, OmpSs-2@Cluster expands the OmpSs-2 programming model to encompass distributed memory clusters. It allows an existing OmpSs-2 program, with few if any changes, to run across multiple nodes. OmpSs-2@Cluster supports transparent multi-node dynamic load balancing for MPI+OmpSs-2 programs, and enables semi-transparent malleability for OmpSs-2@Cluster programs. The runtime system has a high level of stability and performance, and it opens several avenues for future work.(Español) El modelo de programación dominante para clusters tanto en ciencia como industria es actualmente MPI+X. A pesar de que hay alguna variedad de alternativas para programar dentro de un nodo (indicado por la "X"), el estandar para programar múltiples nodos con memoria distribuida sigue siendo Message Passing Interface (MPI). Esta tesis propone la extensión del modelo de programación basado en tareas OmpSs-2 para su funcionamiento en sistemas de memoria distribuida, destacando 3 beneficios principales: En primer lugar; a pequeña y mediana escala, un modelo basado en tareas es más simple y productivo que MPI y elimina la necesidad de distribuir los datos explícitamente y convertir todas las dependencias en mensajes. Además, evita la complejidad de la programacion híbrida MPI+X. En segundo lugar; la capacidad de enviar partes del cálculo entre los nodos permite a la librería balancear la carga de trabajo en programas MPI+X a gran escala. Este enfoque no necesita un modelo de coste y permite equilibrar cargas transversalmente en todo el programa y todos los nodos. En tercer lugar; teniendo en cuenta que es la librería quien maneja todos los aspectos relacionados con distribución y transferencia de datos, es posible la modificación dinámica y transparente de los recursos que utiliza la aplicación. Esta tesis describe el diseño, desarrollo y evaluación de OmpSs-2@Cluster; un modelo de programación y librería que extiende OmpSs-2 permitiendo la ejecución de programas OmpSs-2 existentes en múltiples nodos sin prácticamente necesidad de modificarlos. Para aplicaciones balanceadas, este modelo proporciona un rendimiento similar a MPI+OpenMP hasta 16 nodos y duplica el rendimiento en aplicaciones irregulares o desbalanceadas como la factorización de Cholesky. Este trabajo incluye la extensión de OmpSs-2@Cluster para interactuar con MPI y la librería de balanceo de carga Dynamic Load Balancing (DLB) desarrollada en el Barcelona Supercomputing Center (BSC). De este modo es posible equilibrar aplicaciones MPI+OmpSs-2 mediante la transferencia transparente de tareas entre nodos. Este enfoque reduce el tiempo de ejecución de una aplicación de mecánica de sólidos a micro-escala en un 46% en 64 nodos; en algunos experimentos hasta 8 nodos se pudo equilibrar perfectamente la carga con una diferencia inferior al 10% del equilibrio perfecto. Finalmente, se implementó otra extensión de la librería para realizar operaciones de maleabilidad en programas OmpSs-2@Cluster e interactuar con el Sistema de Manejo de Recursos (RMS). El único cambio requerido en la aplicación es la llamada explicita a una función de la interfaz que controla la adición o eliminación de nodos. Además, se agregó la funcionalidad de guardar y recuperar parte del estado de la aplicación de forma semitransparente con el objetivo de realizar operaciones de salva-reinicio. Dicha funcionalidad oculta al usuario la complejidad de la redistribución de datos y las operaciones de lectura-escritura en paralelo, mientras permite al programa recuperar y continuar ejecuciones previas. Este es un punto de partida para futuras investigaciones en tolerancia a fallos. En resumen, OmpSs-2@Cluster amplía el modelo de programación de OmpSs-2 para abarcar sistemas de memoria distribuida. El modelo permite la ejecución de programas OmpSs-2 en múltiples nodos prácticamente sin necesidad de modificarlos. OmpSs-2@Cluster permite además el balanceo dinámico de carga en aplicaciones híbridas MPI+OmpSs-2 ejecutadas en varios nodos y es capaz de realizar maleabilidad semi-transparente en programas OmpSs-2@Cluster puros. La librería tiene un niveles de rendimiento y estabilidad altos y abre varios caminos para trabajos futuro.Arquitectura de computador

Ordonnancement de tâches parallèles sous multiples ressources : Ordonnancement de Listes vs ordonnancement de Packs

Scheduling in High-Performance Computing (HPC) has been traditionally centered around computing resources (e.g., processors/cores). The ever-growing amount of data produced by modern scientific applications start to drive novel architectures and new computing frameworks to support more efficient data processing, transfer and storage for future HPC systems. This trend towards data-driven computing demands the scheduling solutions to also consider other resources (e.g., I/O, memory, cache) that can be shared amongst competing applications. In this paper, we study the problem of scheduling HPC applications while exploring the availability of multiple types of resources that could impact their performance. The goal is to minimize the overall execution time, or makespan, for a set of moldable tasks under multiple-resource constraints. Two scheduling paradigms, namely, list scheduling and pack scheduling, are compared through both theoretical analyses and experimental evaluations. Theoretically, we prove, for several algorithms falling in the two scheduling paradigms, tight approximation ratios that increase linearly with the number of resource types. As the complexity of direct solutions grows exponentially with the number of resource types, we also design a strategy to indirectly solve the problem via a transformation to a single-resource-type problem, which can significantly reduce the algorithms' running times without compromising their approximation ratios. Experiments conducted on Intel Knights Landing with two resource types (processor cores and high-bandwidth memory) and simulations designed on more resource types confirm the benefit of the transformation strategy and show that pack-based scheduling, despite having a worse theoretical bound, offers a practically promising and easy-to-implement solution, especially when more resource types need to be managed.L'ordonnancement en Calcul Haute-Performance est traditionnellement centré autour des ressources de calculs (processeurs, coeurs). Suite à l'explosion des quantités de données dans les applications scientifiques, de nouvelles architectures et nouveaux paradigmes de calcul apparaissent pour soutenir plus efficacement les calculs dirigés par l'accès aux données. Nous présentons ici des solutions algorithmiques qui prennent en compte cette multitude de ressources