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In this paper, we describe a novel algorithm for dynamic traffic engineering in the Internet called Adaptive Multi-Path routing (AMP). The main objective of AMP is to distribute load within a network domain in a continuous manner by offloading congested links in real-time. The algorithm's recursive signaling structure represents one of our central contributions, as it restricts information exchange to neighboring nodes while still maintaining global propagation of congestion information. This paper starts with a comprehensive survey of related literature, before we introduce AMP in depth and present our exhaustive performance evaluation which is carried out using full implementations of the algorithm both in packet-level and flow-level simulation environments. The investigated state-of-the-art topologies and traffic models provide a detailed insight into the behavior of AMP in realistic operators' networks of substantial size and complexity, whereas our results demonstrate both the traffic engineering efficiency and the stability of AMP. Finally, we present important areas of application for AMP in emerging networking architectures and conclude the paper with an outlook on future research.