Online Scheduling With General Cost Functions

We consider a general online scheduling problem where the goal is to minimize Sigma(j) w(j)g(F-j), where w(j) is the weight/importance of job J(j), F-j is the flow time of the job in the schedule, and g is an arbitrary nondecreasing cost function. Numerous natural scheduling objectives are special cases of this general framework. We show that the scheduling algorithm Highest Density First (HDF) is (2 + epsilon)-speed O(1)-competitive for all cost functions g simultaneously. We give lower bounds that show that the HDF algorithm and this analysis are essentially optimal. Finally, we show that scalable algorithms are achievable in some special cases.