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We present an algorithmic framework for criteria-based segmentation of trajectories that can efficiently process a large class of criteria. Criteria-based segmentation is the problem of subdividing a trajectory into a small number of parts such that each part satisfies a global criterion. Our framework can handle criteria that are stable, in the sense that… (More)

The greedy spanner is a high-quality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner on $$n$$ n points use $$\varOmega (n^2)$$ Ω ( n 2 ) space, which is… (More)

Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms for two geometric problems: computing the convex hull of a… (More)

The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it on n points take $$\varOmega (n^2)$$ Ω ( n 2 ) time, limiting its applicability on large data sets. We propose a novel algorithm design which… (More)

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