Monotone Simultaneous Paths Embeddings in R-d

David Bremner,Olivier Devillers,Marc Glisse,Sylvain Lazard,Giuseppe Liotta,Tamara Mchedlidze,Guillaume Moroz,Sue Whitesides,Stephen Wismath

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE（2018）

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摘要

We study the following problem: Given k paths that share the same labeled vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension d >= 2, there is a set of d + 1 paths that does not admit a monotone simultaneous geometric embedding.

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关键词

graph drawing,point hyperplane duality,high-dimensional space,algorithm

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