We study the problem of minimizing weighted ow t i m e o n a single machine in the preemptive setting. We present an O(log 2 P)-competitive semi-online algorithm where P is the ratio of the maximum and minimum processing times of jobs in the system. In the o ine setting we show that a (2 + )-approximation is achievable in quasi-polynomial time. These are the rst non-trivial results for the weighted versions of minimizing ow t i m e . For multiple machines we show that no competitive randomized online algorithm exists for weighted ow time. We also present an improved online algorithm for minimizing total stretch (a special case of weighted ow time) on multiple machines.
It is known that without speed augmentation there is no competitive online algorithm for minimizing weighted flow time REF .
Algorithms for minimizing weighted flow time
STOC '01
Computer Science