1. Drawing a tree as a minimum spanning tree approximation
- Author
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Di Giacomo, Emilio, Didimo, Walter, Liotta, Giuseppe, and Meijer, Henk
- Subjects
- *
SPANNING trees , *DECISION trees , *APPROXIMATION theory , *EUCLIDEAN algorithm , *PATH analysis (Statistics) , *COMPUTER algorithms - Abstract
Abstract: We introduce and study -EMST drawings, i.e., planar straight-line drawings of trees such that, for any fixed , the distance between any two vertices is at least the length of the longest edge in the path connecting them. -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 -EMST drawing for any given . We also present drawing algorithms that compute -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. [Copyright &y& Elsevier]
- Published
- 2012
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