Abstract of paper by C. Chekuri, S. Khanna, A. Zhu, STOC (2001): We study the problem of minimizing weighted flow time on a single machine in the pre-emptive setting. We present an O(log^2 P) competitive semionline algorithm where P is the ratio of the maximum and minimum processing times of jobs in the system. In the offline setting we show that a (2 + epsilon)approximation is achievable in quasipolynomial time. These are the first nontrivial results for the weighted versions of minimizing flow time. For multiple machines we show that no competitive randomized online algorithm exists for weighted flow time. We also present an improved online algorithm for minimizing total stretch (a special case of weighted flow time) on multiple machines.