Finding a Minimum-depth Embedding of a Planar Graph in O(n 4) Time
- 19 December 2009
- journal article
- Published by Springer Science and Business Media LLC in Algorithmica
- Vol. 60 (4), 890-937
- https://doi.org/10.1007/s00453-009-9380-6
Abstract
Consider an n-vertex planar graph G. The depth of an embedding Γ of G is the maximum distance of its internal faces from the external one. Several researchers pointed out that the quality of a planar embedding can be measured in terms of its depth. We present an O(n 4)-time algorithm for computing an embedding of G with minimum depth. This bound improves on the best previous bound by an O(nlog n) factor. As a side effect, our algorithm improves the bounds of several algorithms that require the computation of a minimum-depth embedding.Keywords
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