Minimizing weighted ℓp-norm of flow-time in the rejection model

We consider the online scheduling problem to minimize the weighted ℓp-norm of flow-time of jobs. We study this problem under the rejection model introduced by Choudhury et al. (SODA 2015) - here the online algorithm is allowed to not serve an "-fraction of the requests. We consider the restricted assignments setting where each job can go to a specified subset of machines. Our main result is an immediate dispatch non-migratory 1/εO(1)-competitive algorithm for this problem when one is allowed to reject at most ε-fraction of the total weight of jobs arriving. This is in contrast with the speed augmentation model under which no online algorithm for this problem can achieve a competitive ratio independent of p.