On Voronoi visibility maps of 1.5D terrains with multiple viewpoints

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00567920" target="_blank" >RIV/67985807:_____/23:00567920 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/23:00366414
Result on the web
<a href="https://doi.org/10.1016/j.ipl.2023.106362" target="_blank" >https://doi.org/10.1016/j.ipl.2023.106362</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2023.106362" target="_blank" >10.1016/j.ipl.2023.106362</a>

Result language
angličtina
Original language name
On Voronoi visibility maps of 1.5D terrains with multiple viewpoints
Original language description
Given an n-vertex 1.5D terrain T and a set P of m < n viewpoints, the Voronoi visibility map VorVis(T,P) is a partitioning of T into regions such that each region is assigned to the closest (in Euclidean distance) visible viewpoint. The colored visibility map ColVis(T, P) is a partitioning of T into regions that have the same set of visible viewpoints. In this paper, we propose an algorithm to compute VorVis(T,P) that runs in O(n + (m2 + kc) log n) time, where kc and kv denote the total complexity of ColVis(T, P) and VorVis(T, P), respectively. This improves upon a previous algorithm for this problem. We also generalize our algorithm to higher order Voronoi visibility maps, and to Voronoi visibility maps with respect to other distances. Finally, we prove bounds relating kv to kc, and we show an application of our algorithm to a problem on limited range of sight.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GJ19-06792Y" target="_blank" >GJ19-06792Y: Structural properties of visibility in terrains and farthest color Voronoi diagrams</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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