Abstract | ||
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Ordered trees are generally drawn using order-preserving planar straight-line grid drawings. We therefore investigate the area-requirements of such drawings, and present several results: Let T be an ordered tree with n nodes. Then: - T admits an order-preserving planar straight-line grid drawing with O(n log n) area. - If T is a binary tree, then T admits an order-preserving planar straight-line grid drawing with O(n log log n) area. - If T is a binary tree, then T admits an order-preserving upward planar straight-line grid drawing with optimal O(n log n) area. We also study the problem of drawing binary trees with user-specified arbitrary aspect ratios. We show that an ordered binary tree T with n nodes admits an order-preserving planar straight-line grid drawing Γ with width O(A + log n), height O((n/A) log A), and area O((A + log n)(n/A) log A) = O(n log n), where 2 ≤ A ≤ n is any user-specified number. Also note that all the drawings mentioned above can be constructed in O(n) time. |
Year | DOI | Venue |
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2003 | 10.1142/S021819590300130X | COCOON |
Keywords | DocType | Volume |
tree, drawing, order-preserving, planar, straight-line | Journal | 13 |
Issue | ISSN | ISBN |
6 | 0218-1959 | 3-540-40534-8 |
Citations | PageRank | References |
3 | 0.48 | 9 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
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Ashim Garg | 1 | 494 | 36.84 |
Adrian Rusu | 2 | 82 | 10.65 |