Treffer: Non-crossing paths with geographic constraints

Title:
Non-crossing paths with geographic constraints
Authors:
Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. CGA - Computational Geometry and Applications, Silveira, Rodrigo Ignacio, Speckmann, Bettina, Verbeek, Kevin
Publisher Information:
Chapman & Hall/CRC 2019-01-01
Document Type:
E-Ressource Electronic Resource
Index Terms:
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, Numerical analysis, non-crossing connectors problem, constrained graph drawing, Anàlisi numèrica, Classificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry, Article
URL:
https://arxiv.org/pdf/1708.05486.pdf
http://hdl.handle.net/2117/174889
https://link.springer.com/chapter/10.1007/978-3-319-73915-1_35
Availability:
Open access content. Open access content
Open Access
Note:
8 p.
application/pdf
English
Other Numbers:
HGF oai:upcommons.upc.edu:2117/174889
Silveira, R.; Speckmann, B.; Verbeek, K. Non-crossing paths with geographic constraints. "Discrete mathematics and theoretical computer science", 1 Gener 2019, vol. 10692, p. 454-461.
1462-7264
10.1007/978-3-319-73915-1_35
1141699353
Contributing Source:
UNIV POLITECNICA DE CATALUNYA
From OAIster®, provided by the OCLC Cooperative.
Accession Number:
edsoai.on1141699353
Database:
OAIster

Weitere Informationen

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
Postprint (author's final draft)