Static scheduling of a program represented by a directed task graph on a multiprocessor system to minimize the program completion time is a well-known problem in parallel processing. Since finding an optimal schedule is an NP-complete problem in general, researchers have resorted to devising efficient heuristics. A plethora of heuristics have been proposed based on a wide spectrum of techniques, including branch-and-bound, integer-programming, searching, graph-theory, randomization, genetic algorithms, and evolutionary methods. The objective of this survey is to describe various scheduling algorithms and their functionalities in a contrasting fashion as well as examine their relative merits in terms of performance and time-complexity. Since these algorithms are based on diverse assumptions, they differ in their functionalities, and hence are difficult to describe in a unified context. We propose a taxonomy that classifies these algorithms into different categories. We consider 27 scheduling algorithms, with each algorithm explained through an easy-to-understand description followed by an illustrative example to demonstrate its operation. We also outline some of the novel and promising optimization approaches and current research trends in the area. Finally, we give an overview of the software tools that provide scheduling/mapping functionalities.

http://charm.cs.uiuc.edu/users/arya/docs/6.pdf

Static scheduling algorithms for allocating directed task graphs to multiprocessors

One measure of the usefulness of a general-purpose distributed computing system is the system's ability to provide a level of performance commensurate to the degree of multiplicity of resources present in the system. A taxonomy of approaches to the resource management problem is presented in an attempt to provide a common terminology and classification mechanism necessary in addressing this problem. The taxonomy, while presented and discussed in terms of distributed scheduling, is also applicable to most types of resource management. >

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A taxonomy of scheduling in general-purpose distributed computing systems

In this paper, we propose a static scheduling algorithm for allocating task graphs to fully connected multiprocessors. We discuss six recently reported scheduling algorithms and show that they possess one drawback or the other which can lead to poor performance. The proposed algorithm, which is called the Dynamic Critical-Path (DCP) scheduling algorithm, is different from the previously proposed algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it selects a suitable processor for a node by looking ahead the potential start times of the remaining nodes on that processor, and schedules relatively less important nodes to the processors already in use. A global as well as a pair-wise comparison is carried out for all seven algorithms under various scheduling conditions. The DCP algorithm outperforms the previous algorithms by a considerable margin. Despite having a number of new features, the DCP algorithm has admissible time complexity, is economical in terms of the number of processors used and is suitable for a wide range of graph structures.

Dynamic critical-path scheduling: an effective technique for allocating task graphs to multiprocessors

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph are presented. >

A genetic algorithm for multiprocessor scheduling

Programming assistance, automation concepts, and their application to a message-passing system program development tool called Hypertool are discussed. Hypertool performs scheduling and handles the communication primitive insertion automatically, thereby increasing productivity and eliminating synchronization errors. Two algorithms, based on the critical-path method, are presented for scheduling processes statically. Hypertool also generates the performance estimates and other program quality measures to help programmers improve their algorithms and programs. >

Hypertool: a programming aid for message-passing systems

This paper describes a set of techniques that can be used to optimally schedule a sequence of interrelated computational tasks on a multiprocessor computer system. Using a directed graph model to represent a computational process, two basic problems are solved here. First, given a set of computational tasks and the relationships between them, the tasks are scheduled such that the total execution time is minimized, and the minimum number of processors required to realize this schedule is obtained. The second problem is of a more general nature. Given k processors, the tasks are scheduled such that execution time is again minimized. Consideration is given to tasks of equal and unequal duration, and task preemption is not allowed.

Optimal Scheduling Strategies in a Multiprocessor System

Recently, several systems have been designed which use reconfigurable logic to perform general purpose computation. While the number of these systems being constructed continues to increase, their relationship to conventional architectures is not clear. This paper proposes a model which unifies traditional instruction set architectures with reconfigurable architectures. From this model, four major architectural categories of reconfigurable machines are given. From this classification, issues of performance, programmability and scalability are addressed.

Classification and Performance of Reconfigurable Architectures

Neural network implementation using reconfigurable architectures

The fast Fourier transform algorithm is specified in a data parallel version of 'C'. This specification is used to produce a custom circuit suitable for use in a system based on reconfigurable logic. Performance estimates indicate that this approach is capable of producing the 2D Fourier transform of images at real time video rates.

FFT on reconfigurable hardware

Recently, several research and commercial systems based on reconfigurable logic have been implemented. These machines have demonstrated supercomputer levels of performance for a number of algorithms. While these demonstrations have been impressive, it is not clear that architectures based on reconfigurable logic will necessarily be suitable for algorithms commonly executed on supercomputers. This paper discusses the implementation of Livermore Fortran Kernels for a supercomputer class machine based on reconfigurable logic.

Mario J. Gonzalez

Papers

Optimal Scheduling Strategies in a Multiprocessor System

Classification and Performance of Reconfigurable Architectures

Neural network implementation using reconfigurable architectures

FFT on reconfigurable hardware

Supercomputing with Reconfigurable Architectures