Recently, a moderate amount of work has been reported on the use of overlay networks to support value-added network services, such as multicasting, Quality of Service (QoS), security, etc. To design an overlay network, the first step is to choose an overlay topology connecting all the overlay service nodes. When considering overlay topologies, several questions need to be answered first: How overlay topologies affect overlay routing performance? Which topologies can provide satisfactory performance? How can we construct efficient overlay topologies connecting all the overlay nodes? In this paper, we focus on the overlay network topology construction issue. First, we evaluate and compare the performance and overhead of the existing overlay topologies. Second, we formalize the overlay topology construction problem and propose two new heuristic methods to construct efficient overlay topologies. Simulation results have demonstrated the efficiency of the two proposed approaches. It is s...