Non-crossing Connectors in the Plane

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190984" target="_blank" >RIV/00216208:11320/13:10190984 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007/978-3-642-38236-9_11" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-642-38236-9_11</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-38236-9_11" target="_blank" >10.1007/978-3-642-38236-9_11</a>

Result language
angličtina
Original language name
Non-crossing Connectors in the Plane
Original language description
We consider the non-crossing connectors problem, which is stated as follows: Given n regions R1 , . . . , Rn in the plane and finite point sets Pi SUBSET OF Ri for i = 1, . . . , n, are there non-crossing connectors yi for (Ri , Pi ), i.e., arc-connectedsets ?i with Pi SUBSET OF ?i SUBSET OF Ri for every i = 1, . . . , n, such that ?i INTERSECTION ?j = EMPTY SET for all i = j? We prove that non-crossing connectors do always exist if the regions form a collection of pseudo-disks, i.e., the boundaries ofevery pair of regions intersect at most twice. We provide a simple polynomial-time algorithm if each region is the convex hull of the corresponding point set, or if all regions are axis-aligned rectangles. We prove that the general problem is NP-hard, even if the regions are convex, the boundaries of every pair of regions intersect at most four times and Pi consists of only two points on the boundary of Ri for i = 1, . . . , n. Finally, we prove that the non-crossing connectors problem
Czech name
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Czech description
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Project
<a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Theory and Applications of Models of Computation; 10th International Conference, TAMC 2013, Hong Kong, China, May 20-22, 2013. Proceedings
ISBN
978-3-642-38235-2
ISSN
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e-ISSN
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Number of pages
13
Pages from-to
108-120
Publisher name
Springer
Place of publication
Berlin
Event location
Hong Kong
Event date
May 20, 2013
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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