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We consider scheduling jobs online to minimize the objective i∈[n] wig(Ci − ri), where wi is the weight of job i, ri is its release time, Ci is its completion time and g is any non-decreasing convex function. Previously, it was known that the clairvoyant algorithm Highest-Density-First (HDF) is (2 +)-speed O(1)-competitive for this objective on a single(More)
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g O(g) n log log n time, matching the running time of the fastest algorithm known for planar graphs, due to Ł ˛ acki and Sankowski, for(More)
With the massive amounts of data available today, it is common to store and process data using multiple machines. Parallel programming platforms such as MapReduce and its variants are popular frameworks for handling such large data. We present the first provably efficient algorithms to compute, store, and query data structures for range queries and(More)
We present the first subquadratic algorithms for computing similarity between a pair of point sequences in R d , for any fixed d > 1, using dynamic time warping (DTW) and edit distance, assuming that the point sequences are drawn from certain natural families of curves. In particular , our algorithms compute (1 + ε)-approximations of DTW and ED in(More)