Pierre-François Dutot

Bi-criteria algorithm for scheduling jobs on cluster platforms

We describe in this paper a new method for building an efficient algorithm for scheduling jobs in a cluster. Jobs are considered as parallel tasks (PT) which can be scheduled on any number of processors. The main feature is to consider two criteria that are optimized together. These criteria are the makespan and the weighted minimal average completion time (minsum). They are chosen for their complementarity, to be able to represent both user-oriented objectives and system administrator objectives.We propose an algorithm based on a batch policy with increasing batch sizes, with a smart selection of jobs in each batch. This algorithm is assessed by intensive simulation results, compared to a new lower bound (obtained by a relaxation of ILP) of the optimal schedules for both criteria separately. It is currently implemented in an actual real-size cluster platform.

Scheduling on hierarchical clusters using malleable tasks

The model of malleable task (MT) was introduced some years ago and has been proved to be an efficient way for implementing parallel applications. It considers a target application at a larger level of granularity than in other models (corresponding typically to numerical routines) where the tasks can themselves be executed in parallel. Clusters of SMP (symmetric Multi-Processors) are a cost effective alternative to parallel supercomputers. Such hierarchical clusters are parallel systems made from m SMP composed each by k identical processors. They are more and more popular, however, designing efficient software that tale full advantage of such systems remains difficult. This work describes a 2 — 2÷k approximation algorithm for scheduling a set of independent malleable tasks for the minimization of the parallel execution time, where k is a power of 2 (k > 2). For k = 2, a special treatment leads to the bound of 3/2 which is the best known for non hierarchical tasks. The algorithm presented here is a fully polynomial approximation scheme running in &Ogr;(nmk) time.

Master-slave tasking on heterogeneous processors

In this paper, we consider the problem of scheduling independent identical tasks on heterogeneous processors where communication times and processing times are different. We assume that communication-computation overlap is possible for every processor, but only allow one send and one receive at a time. We propose an algorithm for chains of processors based on an iterative backward construction of the schedule, which is polynomial in the number of processors and in the number of tasks. The complexity is O(np/sup 2/) where n is the number of tasks and p the number of processors. We prove this algorithm to be optimal with respect to the makespan. We extend this result to a special kind of tree called spider graphs.

A fast 5/2-approximation algorithm for hierarchical scheduling

We present in this article a new approximation algorithm for scheduling a set of n independent rigid (meaning requiring a fixed number of processors) jobs on hierarchical parallel computing platform. A hierarchical parallel platform is a collection of k parallel machines of different sizes (number of processors). The jobs are submitted to a central queue and each job must be allocated to one of the k parallel machines (and then scheduled on some processors of this machine), targeting theminimization of the maximum completion time (makespan). We assume that no job require more resources than available on the smallest machine. This problem is hard and it has been previously shown that there is no polynomial approximation algorithm with a ratio lower than 2 unless P = NP. The proposed scheduling algorithm achieves a 5/2 ratio and runs in O(log(npmax)knlog(n)), where pmax is the maximum processing time of the jobs. Our results also apply for the Multi Strip Packing problem where the jobs (rectangles) must be allocated on contiguous processors.

Combining multiple heuristics on discrete resources

In this work we study the portfolio problem which is to find a good combination of multiple heuristics to solve given instances on parallel resources in minimum time. The resources are assumed to be discrete, it is not possible to allocate a resource to more than one heuristic. Our goal is to minimize the average completion time of the set of instances, given a set of heuristics on homogeneous discrete resources. This problem has been studied in the continuous case in [13]. We first show that the problem is hard and that there is no constant ratio polynomial approximation unless P = NP in the general case. Then, we design several approximation schemes for a restricted version of the problem where each heuristic must be used at least once. These results are obtained by using oracle with several guesses, leading to various tradeoff between the size of required information and the approximation ratio. Some additional results based on simulations are finally reported using a benchmark of instances on SAT solvers.

Scheduling moldable BSP tasks

Our main goal in this paper is to study the scheduling of parallel BSP tasks on clusters of computers. We focus our attention on special characteristics of BSP tasks, which can use fewer processors than the original required, but with a particular cost model. We discuss the problem of scheduling a batch of BSP tasks on a fixed number of computers. The objective is to minimize the completion time of the last task (makespan). We show that the problem is difficult and present approximation algorithms and heuristics. We finish the paper presenting the results of extensive simulations under different workloads.

Scheduling on Large Scale Distributed Platforms: From Models to Implementations

In this paper, we will investigate two complementary computational models that have been proposed recently: Parallel Task (PT) and Divisible Load (DL). The Parallel Task (i.e. tasks that require more than one processor for their execution) model is a promising alternative for scheduling parallel applications, especially in the case of slow communication media. The basic idea is to consider the application at a coarse level of granularity. Another way of looking at the problem (which is somehow a dual view) is the Divisible Load model where an application is considered as a collection of a large number of elementary -- sequential -- computing units that will be distributed among the available resources. Unlike the PT model, the DL model corresponds to a fine level of granularity. We will focus on the PT model, and discuss how to mix it with simple Divisible Load scheduling. As the main difficulty for distributing the load among the processors (usually known as the scheduling problem) in actual systems comes from handling efficiently the communications, these two models of the problem allow us to consider them implicitly or to mask them, thus leading to more tractable problems. We will show that in spite of the enormous complexity of the general scheduling problem on new platforms, it is still useful to study theoretical models. We will focus on the links between models and actual implementations on a regional grid with more than 500 processors.

APPROXIMATION ALGORITHMS FOR MULTIPLE STRIP PACKING AND SCHEDULING PARALLEL JOBS IN PLATFORMS

We consider two strongly related problems, multiple strip packing and scheduling parallel jobs in platforms. In the first one we are given a list of n rectangles with heights and widths bounded by one and N strips of unit width and infinite height. The objective is to find a nonoverlapping orthogonal packing without rotations of all rectangles into the strips minimizing the maximum height used. In the scheduling problem we consider jobs instead of rectangles, i.e., we are allowed to cut the rectangles vertically and we may have target areas of different size, called platforms. A platform Pl is a collection of ml processors running at speed sl and the objective is to minimize the makespan, i.e., the latest finishing time of a job.

Tight Analysis of Relaxed Multi-organization Scheduling Algorithms

The goal of this paper is to study how limited cooperation can impact the quality of the schedule obtained by multiple independent organizations in a typical grid computing platform. This relaxed version of the problem known as the Multi-Organization Scheduling Problem (MOSP) models an environment where organizations providing both resources and jobs tolerate a bounded degradation on the make span of their own jobs in order to minimize the make span over the entire platform. More precisely, the technical contributions are the following. First, we improve the existing in approximation bounds for this problem proving that what was previously though as not polynomially approximable ({\it unless

Scheduling with storage constraints

P=NP