Distortion-Oblivious Algorithms for Scheduling on Multiple Machines

We consider the classic online problem of scheduling on multiple machines to minimize total flow time and total stretch where the input consists of estimates on the processing time provided for each job once released. The performance of such algorithms should depend on µ, the error in the estimates of the processing time for that instance (such an algorithm is called a distortion oblivious algorithm). Previously, a distortion oblivious algorithm to minimize flow time was provided only for a single machine. In this paper we extend the work to multiple machines and also consider the total stretch objective. In particular, we design a non-migrative distortion oblivious algorithm to minimize total flow time with a competitive ratio of O(µlog P), where P is the ratio between the maximum to minimum processing time. We show that with immediate-dispatching one cannot achieve a competitive ratio which is a function of µ and P; moreover, a competitive ratio which is sub-polynomial in the number of jobs is also impossible. We also present the first distortion-oblivious algorithm for minimizing the stretch time, both on a single and on multiple machines. The competitive ratio of these algorithms are O(µ²) which is optimal as we also prove a matching Ω(µ²) lower bound.