I Unidimensional Problems.- 1 Scheduling DAGs without Communications.- 2 Scheduling DAGs with Communications.- 3 Cyclic Scheduling.- II Multidimensional Problems.- 4 Systems of Uniform Recurrence Equations.- 5 Parallelism Detection in Nested Loops.

Scheduling and automatic parallelization

Modern equation-based object-oriented modeling languages which have emerged during the past decades make it easier to build models of large and complex systems. The increasing size and complexity o ...

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Automatic Parallelization of Equation-Based Simulation Programs

Multiprocessor task scheduling is an important and computationally difficult problem. A large number of algorithms were proposed which represent various tradeoffs between the quality of the solution and the computational complexity and scalability of the algorithm. Previous comparison studies have frequently operated with simplifying assumptions, such as independent tasks, artificially generated problems or the assumption of zero communication delay. In this paper, we propose a comparison study with realistic assumptions. Our target problems are two well known problems of linear algebra: LU decomposition and Gauss---Jordan elimination. Both algorithms are naturally parallelizable but have heavy data dependencies. The communication delay will be explicitly considered in the comparisons. In our study, we consider nine scheduling algorithms which are frequently used to the best of our knowledge: min---min, chaining, A*, genetic algorithms, simulated annealing, tabu search, HLFET, ISH, and DSH with task duplication. Based on experimental results, we present a detailed analysis of the scalability, advantages and disadvantages of each algorithm.

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A performance study of multiprocessor task scheduling algorithms

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 $\frac{1}{2}$

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

In Mobile Edge Computing (MEC), many tasks require specific service support for execution and in addition, have a dependent order of execution among the tasks. However, previous works often ignore the impact of having limited services cached at the edge nodes on (dependent) task offloading, thus may lead to an infeasible offloading decision or a longer completion time. To bridge the gap, this article studies how to efficiently offload dependent tasks to edge nodes with limited (and predetermined) service caching. We formally define the problem of offloading dependent tasks with service caching (ODT-SC), and prove that there exists no algorithm with constant approximation for this hard problem. Then, we design an efficient convex programming based algorithm (CP) to solve this problem. Moreover, we study a special case with a homogeneous MEC and propose a favorite successor based algorithm (FS) to solve this special case with a competitive ratio of $O(1)$ O ( 1 ) . Extensive simulation results using Google data traces show that our proposed algorithms can significantly reduce applications’ completion time by about 21-47 percent compared with other alternatives.

Offloading Tasks With Dependency and Service Caching in Mobile Edge Computing

An approximation algorithm for scheduling dependent tasks on m processors with small communication delays

This paper defines and studies an approximation algorithm for scheduling tasks with small communication delays on parallel processors. In a first step, a schedule for the relaxed problem instance with an unlimited number of processors is generated. Then this solution is used to solve the resource conflicts during the scheduling phase on m processors, with a rather unusual feature: a feasible task may be tactically delayed, even inducing idleness on a processor in order to wait for a more important task. The relative worst case performance of this algorithm is analysed with respect to the ratio between communication times and processing times and to the performance of the relaxed solution. It improves significantly the best known performance ratio of an algorithm for this problem (7/3 against 3).

A. Munier

Papers

An approximation algorithm for scheduling dependent tasks on m processors with small communication delays

An approximation algorithm for scheduling dependent tasks on m processors with small communication delays