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hal-00762008, version 1

Non-Linear Divisible Loads: There is No Free Lunch

Olivier Beaumont () 12, Hubert Larchevêque () 12, Loris Marchal () a34

N° RR-8170 (2012)

Abstract: Divisible Load Theory (DLT) has received a lot of attention in the past decade. A divisible load is a perfect parallel task, that can be split arbitrarily and executed in parallel on a set of possibly heterogeneous resources. The success of DLT is strongly related to the existence of many optimal resource allocation and scheduling algorithms, what strongly differs from general scheduling theory. Moreover, recently, close relationships have been underlined between DLT, that provides a fruitful theoretical framework for scheduling jobs on heterogeneous platforms, and \mapreduce, that provides a simple and efficient programming framework to deploy applications on large scale distributed platforms. The success of both have suggested to extend their framework to non-linear complexity tasks. In this paper, we show that both DLT and \mapreduce are better suited to workloads with linear complexity. In particular, we prove that divisible load theory cannot directly be applied to quadratic workloads, such as it has been proposed recently. We precisely state the limits for classical DLT studies and we review and propose solutions based on a careful preparation of the dataset and clever data partitioning algorithms. In particular, through simulations, we show the possible impact of this approach on the volume of communications generated by \mapreduce, in the context of Matrix Multiplication and Outer Product algorithms.

  • a –  CNRS
  • 1:  CEPAGE (INRIA Bordeaux - Sud-Ouest)
  • INRIA – CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)
  • 2:  Laboratoire Bordelais de Recherche en Informatique (LaBRI)
  • CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II
  • 3:  Laboratoire de l'Informatique du Parallélisme (LIP)
  • PRES Université de Lyon – CNRS : UMR5668 – INRIA – École Normale Supérieure (ENS) - Lyon – Université Claude Bernard - Lyon I
  • 4:  ROMA (ENS Lyon / CNRS / Inria Grenoble Rhône-Alpes)
  • INRIA – École Normale Supérieure (ENS) - Lyon – Laboratoire d'informatique du Parallélisme – CNRS : UMR5668
  • Domain : Computer Science/Distributed, Parallel, and Cluster Computing
  • Internal note : RR-8170
  • Comment : accepted for publication in IPDPS 2013
 
  • hal-00762008, version 1
  • oai:hal.inria.fr:hal-00762008
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  • Submitted on: Thursday, 6 December 2012 12:13:32
  • Updated on: Monday, 18 February 2013 19:19:28