Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines

Approximability of Average Completion Time Scheduling on Unrelated Machines

We show that minimizing the average job completion time on unrelated machines isAPX -hard if preemption of jobs is allowed. This provides one of the last missing pieces in the complexity classification of machine scheduling with (weighted) sum of completion times objective. The proof is based on a mixed integer linear program. This means that verification of the reduction is partly done by an I...

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time

Scheduling Multiple Families of Jobs on Parallel Machines to Minimize Total Weighted Completion Time

We consider the problem of scheduling multiple families of jobs on identical parallel machines to minimize the total weighted completion time of the jobs. In this problem, a setup time is necessary whenever a job from one family is processed immediately after another job from a di erent family. The setup time could be sequence independent or sequence dependent. We propose a column generation ba...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

An Online Scalable Algorithm for Minimizing `k-norms of Weighted Flow Time on Unrelated Machines

We consider the problem of scheduling jobs that arrive online in the unrelated machine model to minimize `k norms of weighted flowtime. In the unrelated setting, the processing time and weight of a job depends on the machine it is assigned to, and it is perhaps the most general machine model considered in scheduling literature. Chadha et al. [10] obtained a recent breakthrough result in obtaini...