In this paper, we provide a new class of randomized approximation algorithms for scheduling problems by directly interpreting solutions to so-called time-indexed LPs as probabilities. The most general model we consider is scheduling unrelated parallel machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. The crucial idea for these multi...

Parallel machines concept is a well-known and widely used system in the manufacturing facilities. Scheduling of these parallel machines has been a key activity in the successful product outcome. Though jobs are executed on schedules, in certain cases the completion time increases resulting in tardiness. This survey work identifies and compiles the optimization strategies and solution approaches...

We study the problem of online job-scheduling on parallel machines with di erent network topologies. An online scheduling algorithm schedules a collection of parallel jobs with known resource requirements but unknown running times on a parallel machine. We give an O(plog logN)-competitive algorithm for online scheduling on a two-dimensional mesh of N processors and we prove a matching lower bou...