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Overlay routing in a very attractive scheme that allows improving certain properties of the routing without the need to change the standards of the current underlying routing. However, deploying overlay routing requires the placement and maintenance of overlay infrastructure. This gives rise to the following optimization problem: find a minimal set of overlay nodes such that the required routing properties are satisfied. In this paper we rigorously study this optimization problem. We show that it is NP hard and derive a non-trivial approximation algorithm for it, where the approximation ratio depends on specific properties of the problem at hand. We examine the practical aspects of the scheme by evaluating the gain one can get over two real scenarios. The first one is BGP routing, and we show, using up-to-date data reflecting the current BGP routing policy in the Internet, that a relative small number of less than 100 relay servers are sufficient to enable routing over shorter paths from a single source to all ASes, reducing the average path length of inflated paths by 40%. We also demonstrate that using the scheme for TCP performance improvement, results in an almost optimal placement of overlay nodes.