The influence of lookahead in competitive on-line algorithms

In the competitive analysis of on-line problems, an on-line algorithm is presented with a sequence of requests to be served. The on-line algorithm must satisfy each request without knowledge of any future requests. We consider the question of lookahead in on-line problems: What improvement can be achieved in terms of competitiveness, if the on-line algorithm sees not only the present request but also some future requests? We introduce two different models of lookahead and study the ``classical'' on-line problems such as paging, caching, the $k$-server problem, the list update problem and metrical task systems using these two models. We prove that in the paging problem and the list update problem, lookahead can significantly reduce the competitive factors of on-line algorithms without lookahead. In addition to lower bounds we present a number of on-line algorithms with lookahead for these two problems. However, we also show that in more general on-line problems such as caching, the $k$-server problem and metrical task systems lookahead cannot improve competitive factors of deterministic on-line algorithms without lookahead