GD 2007: Graph Drawing pp 113-124

# Point-Set Embedding of Trees with Edge Constraints

(Extended Abstract)
• Emilio Di Giacomo
• Walter Didimo
• Giuseppe Liotta
• Henk Meijer
• Stephen Wismath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)

## Abstract

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 logn) 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.

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## Authors and Affiliations

• Emilio Di Giacomo
• 1
• Walter Didimo
• 1
• Giuseppe Liotta
• 1
• Henk Meijer
• 2
• Stephen Wismath
• 3
1. 1.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di Perugia