Computational geometry: an introduction
Computational geometry: an introduction
Art gallery theorems and algorithms
Art gallery theorems and algorithms
On the thickness of graphs of given degree
Information Sciences: an International Journal
Straight line embeddings of rooted star forests in the plane
Discrete Applied Mathematics
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
k-colored point-set embeddability of outerplanar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Drawing colored graphs on colored points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Constrained Point-Set Embeddability of Planar Graphs
Graph Drawing
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Given a graph G with n vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S. A geometric point-set embedding is a point-set embedding with no edge bends. This paper studies the following problem: The input is a set S of n points, a planar graph G with n vertices, and a geometric point-set embedding of a subgraph G′ ⊂ G on a subset of S. The desired output is a point-set embedding of G on S that includes the given partial drawing of G′. We concentrate on trees and show how to compute the output in O(n2 log n) time and with at most 1+2⌈k/2⌉ bends per edge, where k is the number of vertices of the given subdrawing. We also prove that there are instances of the problem which require at least k - 3 bends for some of the edges.