# Task scheduling in networks

## Abstract

Scheduling a set of tasks on a set of machines so as to yield an efficient schedule is a basic problem in computer science and operations research. Most of the research on this problem incorporates the potentially unrealistic assumption that communication between the different machines is instantaneous. In this paper, we remove this assumption and study the problem of *network scheduling*, where each job originates at some node of a network, and in order to be processed at another node must take the time to travel through the network to that node.

Our main contribution is to give approximation algorithms and hardness proofs for many of the fundamental problems in network scheduling. We consider two basic scheduling objectives: minimizing the makespan, and minimizing the average completion time. For the makespan we prove small constant factor hardness-to-approximate and approximation results for the most general forms of the problem. For the average completion time, we give a log-squared approximation algorithm; the techniques used in this approximation are somewhat general and have other applications. For example, we give the first non-trivial approximation algorithm to minimize the average completion time of a set of jobs with release dates on identical parallel machines.

Another contribution of this paper is to introduce an interesting class of questions about the design of networks to support specific computational tasks, and to give a polylogarithmic approximation algorithm for one of those problems; specifically, we give approximation algorithms to determine the minimum cost set of machines with which to augment a network so as to make possible a schedule of a certain target length.

## Keywords

Schedule Problem Approximation Algorithm Parallel Machine Schedule Length Identical Parallel Machine## Preview

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