A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks

Authors:
Gregory Mounie;Christophe Rapine;Denis Trystram
Affiliations:
-;-;-
Venue:
SIAM Journal on Computing
Year:
2007

Citing 0
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Abstract

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 $\frac{3}{2}+\varepsilon$ for the minimization of the parallel execution time for any fixed $\varepsilon 0$. 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 $1$ and $\frac{1}{2}$.