Distributed interactive applications may have stringent latency requirements and dynamic user groups. These applications may benefit from a group communication system, and to improve the system support for such applications, we investigate graph algorithms that construct low-latency overlay networks for application-layer multicast. In particular, we focus on reducing the diameter and the pair-wise latencies in the overlay. The overlay construction time is also considered, as it is often time-dependent in our dynamic target applications. Here, we have implemented and experimentally analyzed spanning-tree heuristics and mesh construction heuristics, and compared their performance and applicability to distributed interactive applications. We found that trees are faster to construct and save considerable amounts of resources in the network. Meshes, on the other hand, yield lower pair-wise latencies and increases the fault tolerance, but at the expense of increased resource consumption.