We consider some flow-time minimization problems in the unrelated machines
setting. In this setting, there is a set of m machines and a set of n jobs,
and each job j has a machine dependent processing time of pij on machine
i. The flow-time of a job is the total time the job spends in the system
(completion time minus its arrival time), and is one of the most natural
quality of service measure. We show the following two results: an
O(min(log2n,lognlogP)) approximation algorithm for minimizing the
total-flow time, and an O(logn) approximation for minimizing the maximum
flow-time. Here P is the ratio of maximum to minimum job size. These are the
first known poly-logarithmic guarantees for both the problems.Comment: The new version fixes some typos in the previous version. The paper
is accepted for publication in STOC 201