In overlay networks, when we consider the effective and accurate measurement of underlay IP network between overlay nodes, it is important to take care the density of the overlay nodes in the network. In this paper, we propose the measurement strategy on the overlay networks which dramatically reduces the number of required measurement tasks for obtaining the upto- date characteristics of full-mesh overlay paths. Our method does not require full-mesh information exchange between overlay nodes. One of the advantages of the propose method is that when the number of overlay nodes (N) increases our method does not require O(N2) measurement overhead, and the measurement overhead decreases when the density of the overlay nodes is larger than around 0.5. Through numerical evaluations, we show that our method can reduce the number of required measurements tasks by up to 1/50. We also find that we need to estimate the density of the overlay nodes in the network to determine the length of the measurement cycle for partial overlapping overlay paths.