Point-Set Embeddability of 2-Colored Trees

Frati, Fabrizio and Glisse, Marc and Lenhart, William J. and Liotta, Giuseppe and Mchedlidze, Tamara and Nishat, Rahnuma Islam (2013) Point-Set Embeddability of 2-Colored Trees. In: 20th International Symposium, GD 2012, September 19-21, 2012, Redmond, WA, USA , pp. 291-302 (Official URL: http://link.springer.com/chapter/10.1007/978-3-642-36763-2_26).

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Abstract

In this paper we study bichromatic point-set embeddings of 2-colored trees on 2-colored point sets, i.e., point-set embeddings of trees (whose vertices are colored red and blue) on point sets (whose points are colored red and blue) such that each red (blue) vertex is mapped to a red (resp. blue) point. We prove that deciding whether a given 2-colored tree admits a bichromatic point-set embedding on a given convex point set is an  -complete problem; we also show that the same problem is linear-time solvable if the convex point set does not contain two consecutive points with the same color. Furthermore, we prove a 3n/2 − O(1) lower bound and a 2n upper bound (a 7n/6 − O(logn) lower bound and a 4n/3 upper bound) on the minimum size of a universal point set for straight-line bichromatic embeddings of 2-colored trees (resp. 2-colored binary trees). Finally, we show that universal convex point sets with n points exist for 1-bend bichromatic point-set embeddings of 2-colored trees.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-36763-2_26
Classifications:G Algorithms and Complexity > G.490 Embeddings
ID Code:1318

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