Non-crossing Connectors in the Plane

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-crossing Connectors in the Plane

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Non-crossing Connectors in the Plane

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Kreslení grafů a jejich geometrické reprezentace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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

—

e-ISSN

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Počet stran výsledku

13

Strana od-do

108-120

Název nakladatele

Springer

Místo vydání

Berlin

Místo konání akce

Hong Kong

Datum konání akce

20. 5. 2013

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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