Non-crossing paths with geographic constraints

A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings? We focus on the seemingly simple setting whe...

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Bibliographic Details
Main Authors:	Silveira, Rodrigo Ignacio, Speckmann, Bettina, Verbeek, Kevin
Format:	Publication
Language:	English
Published:	Chapman & Hall/CRC 01.01.2019
Subjects:	65 Numerical analysis 65D Numerical approximation and computational geometry Anàlisi numèrica Classificació AMS constrained graph drawing Matemàtiques i estadística Mètodes numèrics non-crossing connectors problem Numerical analysis Àrees temàtiques de la UPC
ISSN:	1462-7264
Online Access:	Get full text
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Summary:	A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings? We focus on the seemingly simple setting where each region is a unit length vertical segment, and one wants to connect pairs of segments with a path that lies inside the convex hull of the two segments. We prove that when paths must be drawn as straight line segments, it is NP-complete to determine if a crossing-free solution exists. In contrast, we show that when paths must be monotone curves, the question can be answered in polynomial time. In the more general case of paths that can have any shape, we show that the problem is polynomial under certain assumptions. Peer Reviewed
ISSN:	1462-7264
DOI:	10.1007/978-3-319-73915-1_35