Two short notes on the on-line travelling salesman: handling times and lookahead

AbstractWe study extensions of the on-line travelling salesman problem. Our results are: The optimal competitive ratio 2 for arbitrary metric spaces also holds in the case of nonzero handling times. The optimal competitive ratio 3/2 on the half-line cannot be improved by randomization, but there is a 4/3-competitive algorithm under the assumption that the server is notified when the last request has been released. This ratio is also optimal