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Due to the heterogeneity of the environment, in which hosts may have different bandwidth capacities and network distances between hosts vary, current mesh-based multicast protocols for video streaming over the Internet tend to in efficiently utilise the available bandwidth and often transfer large amounts of data between distant hosts. This limits system throughput, which results in reduced video quality, and imposes significant costs on Internet service providers (ISPs) caused by network traffic outside a provider's own network. This paper presents MeshTV, a mesh-based peer-to-peer (P2P) multicast protocol for streaming live video from a transmitter to numerous viewers. MeshTV proposes an algorithm for adapting the mesh overlay in which nodes explore their possible neighbour nodes and select neighbours so that data throughput is optimised and data is transmitted between nearby (low-latency) nodes, typically within the same ISP thus reducing the costs to ISPs. Our evaluation demonstrates that the adaptation algorithm used in MeshTV can improve video streaming throughput by over 100 % and typically reduces the distances (network latencies) between interacting nodes by 50 % compared to unoptimised mesh overlays.