# Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
3 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We study the following problem: Given $k$ paths that share the same 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 $d\geq 2$, there is a set of $d + 1$ paths that does not admit a monotone simultaneous geometric embedding.
Document type :
Conference papers

Cited literature [14 references]

https://hal.inria.fr/hal-01366148
Contributor : Olivier Devillers <>
Submitted on : Wednesday, September 14, 2016 - 10:37:17 AM
Last modification on : Friday, September 20, 2019 - 4:56:35 PM

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### Identifiers

• HAL Id : hal-01366148, version 1
• ARXIV : 1608.08791

### Citation

David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, et al.. Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$. 24th International Symposium on Graph Drawing & Network Visualization, Sep 2016, Athens, Greece. ⟨hal-01366148⟩

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