Large-scale distributed systems gather thousands of peers spread all over the world. Such systems need to offer good routing performances regardless of their size and despite high churn rates. To achieve that requirement, the system must add appropriate shortcuts to its logical graph (overlay). However, to choose efficient shortcuts, peers need to obtain information about the overlay topology. In case of heterogeneous peer distributions, retrieving such information is not straightforward. Moreover, due to churn, the topology rapidly evolves, making gathered information obsolete. State of- the-art systems either avoid the problem by enforcing peers to adopt a uniform distribution or only partially fulfill these requirements. To cope with this problem, we propose DONUT, a mechanism to build a local map that approximates the peer distribution, allowing the peer to accurately estimate graph distance to other peers with a local algorithm. The evaluation performed with real latency and churn traces shows that our map increases the routing process efficiency by at least 20% compared to the state-of-the-art techniques. It points out that each map is lightweight and can be efficiently propagated through the network by consuming less than 10 bps on each peer.