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The highest quality geometric spanner (e.g. in terms of edge count, both in theory and in practice) known to be computable in polynomial time is the greedy spanner. The state-of-the-art in computing this spanner are a O(n2 log n) time, O(n2) space algorithm and a O(n2 log2 n) time, O(n) space algorithm, as well as the 'improved greedy' algorithm, taking… (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)

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)

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)

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