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Overlay networks have been viewed as one of promising intermediary solutions to provide a supplement with strengthened performance to the existing “best efforts” Internet. Previous researches have shown that overlays constructed taking into consideration of the underlying network topology information perform better than those oblivious to those information. In this paper, we first propose a novel heuristic algorithm to solve the provider-independent overlay construction issue given accurate underlying topological information. However, exact physical topology is usually shielded from the Internet users especially in multiple-domain scenarios and difficult to obtain. One of the issues is the Anonymous Routers (AR) presence in the Internet Thus only inaccurate underlying topologies can be obtained. Even if AR resolution algorithms are implemented, there is no guarantee that it can infer an accurate topology. Therefore, we take a step further to study the impact of inaccurate underlying topological information on overlay topology construction. Initial results obtained show that the availability and accuracy of underlying topology information has impact on its effectiveness in constructing a good overlay topology and cautions are needed when taking advantage of the acquired inaccurate underlying topology information.