Minimizing the total completion time on-line on a single machine, using restarts

We give an algorithm to minimize the total completion time on-line on a single machine, using restarts, with a competitive ratio of 3/2. The optimal competitive ratio without using restarts is 2 for deterministic algorithms and $e/(e-1) approx 1.582$ for randomized algorithms. This is the first restarting algorithm to minimize the total completion time that is proved to be better than an algorithm that does not restart.