Denis Trystram

APPROXIMATION ALGORITHMS FOR SCHEDULING MALLEABLE TASKS UNDER PRECEDENCE CONSTRAINTS

This work presents approximation algorithms for scheduling the tasks of a parallel application that are subject to precedence constraints. The considered tasks are malleable which means that they may be executed on a varying number of processors in parallel. The considered objective criterion is the makespan, i.e., the largest task completion time. We demonstrate a close relationship between this scheduling problem and one of its subproblems, the allotment problem. By exploiting this relationship, we design a polynomial time approximation algorithm with performance guarantee arbitrarily close to for the special case of series parallel precedence constraints and for the special case of precedence constraints of bounded width. These special cases cover the important situation of tree structured precedence constraints. For arbitrary precedence constraints, we give a polynomial time approximation algorithm with performance guarantee .

Random graph generation for scheduling simulations

In parallel and distributed systems, validation of scheduling heuristics is usually done by simulation on randomly generated synthetic workloads, typically represented by task graphs. Since there is no single generation method that models all possible workloads for scheduling problems, researchers often re-implement the classical generation algorithms or even implement ad hoc ones. A bad choice of generation method can mislead the validation of the algorithm due to biases it can induce. Moreover, different implementations of the same randomized generation method may produce slightly different graphs. These problems can harm the experimental comparison of scheduling algorithms. In order to provide a comparison basis we propose GGen -- a unified and standard implementation of classical task graph generation methods used in the scheduling domain. We also provide an in-depth analysis of each generation method, emphasizing important graph properties that may influence scheduling algorithms.

Preemptable malleable task scheduling problem

The problem of optimal scheduling n independent malleable tasks in a parallel processor system is studied. It is assumed that an execution of any task can be preempted and the number of processors allocated to the same task can change during its execution. We present a rectangle packing algorithm, which converts an optimal solution for the relaxed problem, in which the number of processors allocated to a task is not required to be integer, into an optimal solution for the original problem in O(n) time.

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A malleable task is a computational unit that may be executed on any arbitrary number of processors, whose execution time depends on the amount of resources allotted to it. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guarantee of

\frac32

\frac{3}{2}+\varepsilon

-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks

for the minimization of the parallel execution time for any fixed

Handbook on Parallel and Distributed Processing

\varepsilon > 0

A flexible checkpoint/restart model in distributed systems

. The main idea of this approach is to focus on the determination of a good allotment and then to solve the resulting problem with a fixed number of processors by a simple scheduling algorithm. The first phase is based on a dual approximation technique where the allotment problem is expressed as a knapsack problem for partitioning the set of tasks into two shelves of respective heights

Bi-criteria algorithm for scheduling jobs on cluster platforms

1

Scheduling a divisible task in a two-dimensional toroidal mesh

and