TIME: 1:30-2:20 pm, October 9, 2007 PLACE: MGH 295 SPEAKER: Yury Makarychev Microsoft Research TITLE: Local-Global Tradeoffs in Metric Embeddings ABSTRACT: Suppose that every k points in an n point metric space X are D-distortion embeddable into l_1. We give upper and lower bounds on the distortion required to embed the entire space X into l_1. This is a natural mathematical question and is also motivated by the study of relaxations obtained by lift-and-project methods for graph partitioning problems. In this setting, we show that X can be embedded into l_1 with distortion O(D log (n/k)). Moreover, we give a lower bound showing that this result is tight if D is bounded away from 1. For D = 1 + delta we give a lower bound of Omega(log (n/k) / log (1/delta)); and for D=1, we give a lower bound of Omega(log n/(log k + log log n)). Our bounds improve on the results of Arora, Lovasz, Newman, Rabani, Rabinovich and Vempala, who initiated a study of these questions. Joint work with Moses Charikar and Konstantin Makarychev.