Our thesis is that a peer-to-peer networks overlay topology should adapt to match the demand graph of the peer-to-peer network. In order to assess the effectiveness of various adaptation mechanisms, a comparison with an optimal topology for a given demand graph would be helpful. However, several related optimization/decision problems have been shown to be NP-hard. The contributions of this paper are threefold: i) we briefly survey NP-hardness results related to assessing overlay adaptation strategies, ii) we present a specific optimization problem and metric, and iii) we provide experimental results indicating the potential of optimizing the overlay topology. Finally, in the spirit of a challenge paper we state and discuss various open issues.