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Large-scale live media streaming is a challenge for traditional server-based approaches. To appropriately support big audiences, broadcasters must be able to allocate huge bandwidth and computational resources. The costs involved with such an infrastructure exclude all but the established content producers from exploiting the Internet as a distribution medium. Publishers of not-yet-popular content, unless they manage to properly predict their maximum audience size, will likely fail to dimension correctly their broadcast infrastructure. Peer-to-peer systems for live streaming allow the users to support content distribution by contributing their unused resources: this increases the scalability of the content distribution while reducing at the same time the economical burden on the streaming provider. This paper presents and evaluates PULSE, an unstructured mesh-based peer-to-peer system designed to support live streaming to large audiences under the arbitrary resource availability as is typically the case for the Internet. PULSE is a highly dynamic system: it constantly optimizes its mesh of data connections using a feedback-driven peer selection strategy that is based on pairwise incentives. We evaluate the behavior of PULSE under realistic scenarios via simulation and emulation, and present the advantages of our approach, namely a best-effort response to system-wide resource scarcity, high resilience to node churn, and good hop-count properties of the average data distribution paths.