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- Angelini, P., et al.
(author)
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On the area requirements of Euclidean minimum spanning trees
- 2014
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In: Computational geometry. - : Elsevier. - 0925-7721 .- 1879-081X. ; 47:2, s. 200-213
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Journal article (peer-reviewed)abstract
- In their seminal paper on Euclidean minimum spanning trees, Monma and Suri (1992) proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that there exist n-vertex trees of maximum degree 5 that require c(n) x c(n) area to be embedded as Euclidean minimum spanning trees, for some constant c > 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.
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- Angelini, P., et al.
(author)
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On the area requirements of Euclidean minimum spanning trees
- 2011
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In: Algorithms and Data Structures. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642222993 ; , s. 25-36
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Conference paper (peer-reviewed)abstract
- In their seminal paper on Euclidean minimum spanning trees [Discrete & Computational Geometry, 1992], Monma and Suri proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that c(n) x c(n) area is sometimes required to embed an n-vertex tree of maximum degree 5 as a Euclidean minimum spanning tree, for some constant c > 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.
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