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Several push-pull hybrid peer-to-peer (P2P) video live streaming schemes introduce data-driven push trees into the pull scheme and have a short playback delay while being robust against peer churn, but the substrate Internet utilization remains unaddressed. In this paper, we propose TreeClimber, a network-driven robust push-pull scheme for large-scale P2P video live streaming applications. The scheme first constructs a neighbourhood overlay with short edges and a small diameter, then uses a robust distributed algorithm to build a short tree on the overlay. We have implemented a discrete-event simulator to examine TreeClimber and a comparative data-driven scheme. Results show that TreeClimber achieves high network utilization while having better or similar playback delay and robustness.