Special cases of online parallel job scheduling

In this paper we consider the online scheduling of jobs, which require processing on a number of machines simultaneously. These jobs are presented to a decision maker one by one, where the next job becomes known as soon as the current job is scheduled. The objective is to minimize the makespan. For the problem with three machines we give a 2.8-competitive algorithm, improving upon the 3-competitive greedy algorithm. For the special case with arbitrary number of machines, where the jobs appear in non-increasing order of machine requirement, we give a 2.4815-competitive algorithm, improving the 2.75-competitive greedy algorithm

Job Scheduling Using successive Linear Programming Approximations of a Sparse Model

EuroPar 2012In this paper we tackle the well-known problem of scheduling a collection of parallel jobs on a set of processors either in a cluster or in a multiprocessor computer. For the makespan objective, i.e., the completion time of the last job, this problem has been shown to be NP-Hard and several heuristics have already been proposed to minimize the execution time. We introduce a novel approach based on successive linear programming (LP) approximations of a sparse model. The idea is to relax an integer linear program and use lp norm-based operators to force the solver to find almost-integer solutions that can be assimilated to an integer solution. We consider the case where jobs are either rigid or moldable. A rigid parallel job is performed with a predefined number of processors while a moldable job can define the number of processors that it is using just before it starts its execution. We compare the scheduling approach with the classic Largest Task First list based algorithm and we show that our approach provides good results for small instances of the problem. The contributions of this paper are both the integration of mathematical methods in the scheduling world and the design of a promising approach which gives good results for scheduling problems with less than a hundred processors

Algorithmes d’ordonnancement des tâches dans un environnement Cloud

Les systèmes distribués à grande échelle comme les Grilles ou les Nuages (Clouds) [8] sont fondamentalement dynamiques et instables, et il est également réaliste de considérer que certaines ressources vont subir des défaillances pendant leur utilisation. La panne d’une ressource peut affecter l’entière exécution des applications qui nécessitent la disponibilité de plusieurs ressources en même temps. Afin de pouvoir gérer des plates-formes dynamiques à grande échelle, il faut se tourner vers des algorithmes d'ordonnancement et d'équilibrage de charge décentralisés, de telle sorte que le système puisse passer à l'échelle, sans que les performances de la plate-forme soient limitées par celle du noeud en charge de l'ordonnancement. Dans ce papier, nous présentons un état de l’art sur les algorithmes d'ordonnancement et d'équilibrage de charge destinés pour les Clouds. Nous proposons comme synthèse une classification de ces algorithmes sur la base de critères et de dimensions que nous avons définis à cet effet

A Survey of Classical and Recent Results in Bin Packing Problem

In the classical bin packing problem one receives a sequence of n items 1, 2,..., n with sizes s1, s2, . . . ,sn where each item has a fixed size in (0, 1]. One needs to find a partition of the items into sets of size1, called bins, so that the number of sets in the partition is minimized and the sum of the sizes of the pieces assigned to any bin does not exceed its capacity. This combinatorial optimization problem which is NP hard has many variants as well as online and offline versions of the problem. Though the problem is well studied and numerous results are known, there are many open problems. Recently bin packing has gained renewed attention in as a tool in the area of cloud computing. We give a survey of different variants of the problem like 2D bin packing, strip packing, bin packing with rejection and emphasis on recent results. The thesis contains a discussion of a newly claimed tight result for First Fit Decreasing by Dosa et.al. as well as various new versions of the problem by Epstein and others