Scheduling search procedures

We analyze preemptive on-line scheduling against randomized adversaries, with the goal to finish an unknown distinguished target job. Our motivation comes from clinical gene search projects, but the subject leads to general theoretical questions of independent interest, including some natural but unusual probabilistic models. We study problem versions with known and unknown processing times of jobs and target probabilities, and models where the on-line player gets some randomized extra information about the target. For some versions we get optimal competitive ratios, expressed in terms of given parameters of instances.