Abstract
We introduce and study (1 + ε)-EMST drawings, i.e. planar straight-line drawings of trees such that, for any fixed ε> 0, the distance between any two vertices is at least \(\frac{1}{1 + \varepsilon}\) the length of the longest edge in the path connecting them. (1 + ε)-EMST drawings are good approximations of Euclidean minimum spanning trees. While it is known that only trees with bounded degree have a Euclidean minimum spanning tree realization, we show that every tree T has a (1 + ε)-EMST drawing for any given ε> 0. We also present drawing algorithms that compute (1 + ε)-EMST drawings of trees with bounded degree in polynomial area. As a byproduct of one of our techniques, we improve the best known area upper bound for Euclidean minimum spanning tree realizations of complete binary trees.
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Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H. (2010). Drawing a Tree as a Minimum Spanning Tree Approximation. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_6
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DOI: https://doi.org/10.1007/978-3-642-17514-5_6
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