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The key to optimizing the performance of an anycast-based sys- tem (e.g., the root DNS or a CDN) is choosing the right set of sites to announce the anycast prefix. One challenge here is predicting catchments. A naïve approach is to advertise the prefix from all subsets of available sites and choose the best-performing subset, but this does not scale well. We demonstrate that by conducting pairwise experiments between sites peering with tier-1 networks, we can predict the catchments that would result if we announce to any subset of the sites. We prove that our method is effective in a simplified model of BGP, consistent with common BGP routing policies, and evaluate it in a real-world testbed. We then present AnyOpt, a system that predicts anycast catchments. Using AnyOpt, a network operator can find a subset of anycast sites that minimizes client latency without using the naïve approach. In an experiment using 15 sites, each peering with one of six transit providers, AnyOpt predicted site catchments of 15,300 clients with 94.7% accuracy and client RTTs with a mean error of 4.6%. AnyOpt identified a subset of 12 sites, announcing to which lowers the mean RTT to clients by 33ms compared to a greedy approach that enables the same number of sites with the lowest average unicast latency.