SCHEDULING TO MINIMIZE AVERAGE COMPLETION-TIME - OFF-LINE AND ONLINE APPROXIMATION ALGORITHMS

In this paper we introduce two general techniques for the design and a nalysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the job comple tion times. For a variety of scheduling models, these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum. In t he first approach, we use an optimal solution to a linear programming relaxation in order to guide a simple list-scheduling rule. Consequent ly, we also obtain results about the strength of the relaxation. Our s econd approach yields on-line algorithms for these problems: in this s etting, we are scheduling jobs that continually arrive to be processed and, for each time t, we must construct the schedule until time t wit hout any knowledge of the jobs that will arrive afterwards. Our on-lin e technique yields constant performance guarantees for a variety of sc heduling environments, and in some cases essentially matches the perfo rmance of our off-line LP-based algorithms.