Designing networks incrementally

We consider the problem of incrementally designing a network to route demand to a single sink on an underlying metric space. We are given cables whose costs per unit length scale in a concave fashion with capacity. Under certain natural restrictions on the costs (called the Access Network Design constraints), we present a simple and efficient randomized algorithm that is competitive to the minimum cost solution when the demand points arrive online. In particular, if the order of arrival is a random permutation, we can prove a O(1) competitive ratio. For the fully adversarial case, the algorithm is O(K) -competitive, where K is the number of different pipe types. Since the value of K is typically small, this improves the previous O(log n log log n)-competitive algorithm which was based on probabilistically approximating the underlying metric by a tree metric. Our algorithm also improves the best known approximation ratio and running time for the offline version of this problem.