Lower bounds for randomized k-server and motion-planning algorithms

The authors prove, against an oblivious adversary, 1. an Ω(log k) lower bound on the competitive ration of any randomized on-line k-server algorithm in any sufficiently large metric space. 2. an Ω(log log k) lower bound on the competitive ration of any randomized on-line k-server algorithm in any metric space with at least k+1 points, and 3. an Ω(log log n) lower bound on the competitive ratio of any on-line motion-planning algorithm for a scene with n obstacles.