Task assignment in homogeneous linear network

Abstract

In this thesis, we investigate the problem of task assignment in distributed computer system. The task assignment problem is unavoidable whenever we use distributed program composed of several task modules communicating each other on several computers connected each other. The motives of distributing program by task modules varies from taking benefits of specialized computing environment to integrating computing power of processor elements in the network. We shall confine our domain as benefits of specialized computing. The distribution of a program takes some overhead from interprocess communication. There is a trade-off between communication and computation. The objective function of our model is based on the minimization of total execution and communication costs. It was proven for the graph theoretic method will find an efficient algorithm to assign tasks to processors. This method was limited to 2 processor model. Recently it was extended to n-processor with limited topology. In this thesis, some meta-properties of homogeneous network is exploited: (1) What kind of topology has efficient task assignment algorithm. (2) What is the criterion to distinguish easier graph. (3) How to use the pronciples of the criterion. This is modeled as the existence of a set of useful partitions over processor network which have approachability, convergency. If every node in the network is identifiable by the useful partitions, the network is reducible to two terminal problem. The existence of useful partition depends on the topology of the network. If the network has cycles, the network may be not reducible. This model shows that some regular graph such as tree, k-dimensional mesh, is reducible to two terminal problem. Some irregular graph obtained from deleting several communication links from regular graphs is also reducible. We apply the result of homogeneous network problem to the task assignment problem is heterogeneous network whose processor element has different com...