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Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for k-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of 9+≥ilon, a ratio that is known to be tight with respect to such methods.We overcome this barrier...
We endeavor to assess the impact of introduction of guidelines for preoperative investigations (PIs) on anesthetic practices and costs and compare their efficacy to current practices.A prospective study.Queen Elizabeth Hospital, Barbados.Participants comprised all patients undergoing general, epidural, spinal, and regional anesthesia, with the exception of emergency cases or instances where an anesthesiologist...
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algorithms for these problems. However, these results suffer from high number of rounds, suboptimal approximation ratios, or both. We develop a framework...
Submodular maximization and set systems play a major role in combinatorial optimization. It is long known that the greedy algorithm provides a 1/(k + 1)-approximation for maximizing a monotone submodular function over a k-system. For the special case of k-matroid intersection, a local search approach was recently shown to provide an improved approximation of 1 / (k + δ) for arbitrary δ > 0. Unfortunately,...
We present an optimal, combinatorial 1-1/e approximation algorithm for monotone sub modular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is extremely simple and requires no rounding. It consists of the greedy algorithm followed by local search. Both phases are run not on the actual objective function,...
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