Randomized Approximation Schemes for Scheduling Unrelated Parallel Machines

We consider the problem of Scheduling n Independent Jobs on m Unrelated Parallel Machines, when the number of machines m is xed. We address the standard problem of minimizing the makespan of the schedule (SUM) and the bicriteria problem of scheduling with bounded makespan and cost (SUMC) and show for them randomized fully linear time approximation schemes. While matching the approximation guarantee and the complexity of the best known sequential results of Jansen and Porkolab ( 12]), the proposed algorithms exhibit a signi cantly simpler and more general rounding scheme, especially for the bicriteria SUMC problem, and admit simple optimal work parallelizations1 of O(logn){time complexity. The core of the algorithms, which also draw techniques from other related works ( 12], 11], 1]), is an interesting new randomized rounding procedure, the Filtered Randomized Rounding (FRR). In the settings of the problems considered, FRR boosts the deviation bounds of the rounded linear packing const...

• Type: Journal
• Year: 2000
• Where: ECCC
• Authors: Pavlos Efraimidis, Paul G. Spirakis
• Keywords: ECCC 2000, Linear Time Approximation, Simple Optimal, Time Approximation Schemes