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Many applications in scientific and engineering domains are structured as large numbers of independent tasks with low granularity. These applications are thus amenable to straightforward parallelization, typically in master-worker fashion, provided that efficient scheduling strategies are available. Such applications have been called divisible loads because a scheduler may divide the computation among worker processes arbitrarily, both in terms of number of tasks and of task sizes. Divisible load scheduling has been an active area of research for the last twenty years. A vast literature offers results and scheduling algorithms for various models of the underlying distributed computing platform. Broad surveys are available that report on accomplishments in the field. By contrast, in this paper we propose a unified theoretical perspective that synthesizes previously published results, several novel results, and open questions, in a view to foster novel divisible load scheduling research. Specifically, we discuss both one-round and multi-round algorithms, and we restrict our scope to the popular star and tree network topologies, which we study with both linear and affine cost models for communication and computation.Keywords: parallel computing, scheduling, divisible load Résumé De nombreuses applications scientifiques se découpent naturellement en un grand nombre de tâches indépendantes avec une faible granularité. Ces applications se parallélisent naturellementà l'aide d'une approche maître/esclave. De telles applications relèvent du modèle des tâches divisibles car un ordonnanceur peut diviser les calculs sur les différents processeurs disponibles,à la fois en terme de nombre de tâches maiś egalement en terme de taille des tâches. L'ordonnancement de tâches divisibles aété un domaine de recherche actif durant les vingts dernières années. On trouve donc dans la littérature de nombreux résultats et algorithmes d'ordonnancement pour différents modèles de plates-formes. A la différence desétats de l'art déja existant sur le sujet, ce rapport propose une nouvelle approche permettant d'unifier et de retrouver les résultats de la littérature, de proposer de nouveaux résultats et d'ouvrir de nouveaux problèmes. Plus précisément, nous présentons les distributions en une seule tournée et en plusieurs tournées et nous restreignons aux topologies populaires enétoile et en arborescence, que nous nouś etudionsà l'aide de coût de calculs et de communications linéaires puis affines.

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In this paper, we propose the design of VoroNet, an objectbased peer to peer overlay network relying on Voronoi tessellations, along with its theoretical analysis and experimental evaluation. VoroNet differs from previous overlay networks in that peers are application objects themselves and get identifiers reflecting the semantics of the application instead of relying on hashing functions. This enables a scalable support for efficient search in large collections of data. In VoroNet, objects are organized in an attribute space according to a Voronoi diagram. VoroNet is inspired from the Kleinberg's small-world model where each peer gets connected to close neighbours and maintains an additional pointer to a long-range neighbour. VoroNet improves upon the original proposal as it deals with general object topologies and therefore copes with skewed data distributions. We show that VoroNet can be built and maintained in a fully decentralized way. The theoretical analysis of the system proves that routing in VoroNet can be achieved in a poly-logarithmic number of hops in the size of the system. The analysis is fully confirmed by our experimental evaluation by simulation.

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In this paper, we discuss several algorithms for scheduling divisible loads on heterogeneous systems. Our main contributions are (i) new optimality results for single-round algorithms and (ii) the design of an asymptotically optimal multi-round algorithm. This multi-round algorithm automatically performs resource selection, a difficult task that was previously left to the user. Because it is periodic, it is simpler to implement, and more robust to changes in the speeds of the processors and/or communication links. On the theoretical side, to the best of our knowledge, this is the first published result assessing the absolute performance of a multi-round algorithm. On the practical side, extensive simulations reveal that our multi-round algorithm outperforms existing solution on a large variety of platforms, especially when the communication-to-computation ratio is not very high (the difficult case).

Our goal is to provide an analysis and comparison of static and dynamic strategies for task graph scheduling on platforms consisting of heterogeneous and unrelated resources, such as GPUs and CPUs. Static scheduling strategies, that have been used for years, suffer several weaknesses. First, it is well known that underlying optimization problems are NP-Complete, what limits the capability of finding optimal solutions to small cases. Second, parallelism inside processing nodes makes it difficult to precisely predict the performance of both communications and computations, due to shared resources and co-scheduling effects. Recently, to cope with this limitations, many dynamic task-graph based runtime schedulers (StarPU, StarSs, QUARK, PaRSEC) have been proposed. Dynamic schedulers base their allocation and scheduling decisions on the one side on dynamic information such as the set of available tasks, the location of data and the state of the resources and on the other hand on static information such as task priorities computed from the whole task graph. Our analysis is deep but we concentrate on a single kernel, namely Cholesky factorization of dense matrices on platforms consisting of GPUs and CPUs. This application encompasses many important characteristics in our context. Indeed, it involves 4 different kernels (POTRF, TRSM, SYRK and GEMM) whose acceleration ratios on GPUs are strongly different (from 2.3 for POTRF to 29 for GEMM) and it consists in a phase where the number of available tasks if large, where the careful use of resources is critical, and in a phase with few tasks available, where the choice of the task to be executed is crucial. In this paper, we analyze the performance of static and dynamic strategies and we propose a set of intermediate strategies, by adding more static (resp. dynamic) features into dynamic (resp. static) strategies. Our conclusions are somehow unexpected in the sense that we prove that static-based strategies are very efficient, even in a context where performance estimations are not very good.