6 Search Results for "Mantas, Ioannis"

Artifact
Software
DOI: 10.4230/artifacts.26033
RVD-explorer

Authors: Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland

Abstract
Cite as

Carlos Alegría, Ioannis Mantas, Marko Savić, Martin Suderland. RVD-explorer (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26033,
   title = {{RVD-explorer}}, 
   author = {Alegr{\'\i}a, Carlos and Mantas, Ioannis and Savi\'{c}, Marko and Suderland, Martin},
   note = {Software, version 0.1.0., swhId: \href{https://archive.softwareheritage.org/swh:1:dir:ecbbe02e948195b997416d5a9fd082d6f6c1a01d;origin=https://github.com/VD-collective/rvd-explorer;visit=swh:1:snp:8f902e4373d5eb8fbcd876bdc7c325142a757c65;anchor=swh:1:rev:dd2bdbcf990b964fca72a90757fd18916e2524a5}{\texttt{swh:1:dir:ecbbe02e948195b997416d5a9fd082d6f6c1a01d}} (visited on 2026-05-27)},
   url = {https://github.com/VD-collective/rvd-explorer},
   doi = {10.4230/artifacts.26033},
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.98
Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition)

Authors: Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Floodlight illumination problems are art-gallery variants, where a target domain needs to be illuminated by guards, each associated with a field of view. The rotating rays Voronoi diagram is a Voronoi diagram with rays as sites under the angular distance. There is a natural connection of this Voronoi structure with the problem of finding the minimum aperture such that a given set of uniform aperture floodlights illuminates a target domain. In this work we present an interactive visualization software for such problems, supporting different angular distances, namely, oriented and unoriented versions, and for different domains, namely, the plane and simple polygons.
Cite as

Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland. Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 98:1-98:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alegria_et_al:LIPIcs.SoCG.2026.98,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Savi\'{c}, Marko and Suderland, Martin},
  title =	{{Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{98:1--98:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.98},
  URN =		{urn:nbn:de:0030-drops-259048},
  doi =		{10.4230/LIPIcs.SoCG.2026.98},
  annote =	{Keywords: rotating rays Voronoi diagram, oriented angular distance, unoriented angular distance, Brocard angle, floodlight illumination, coverage problems, visualization software}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.12
Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework

Authors: Sang Won Bae, Nicolau Oliver, and Evanthia Papadopoulou

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a set S of n colored sites, each s ∈ S associated with a distance-to-site function δ_s : ℝ² → ℝ, we consider two distance-to-color functions for each color: one takes the minimum of δ_s for sites s ∈ S in that color and the other takes the maximum. These two sets of distance functions induce two families of higher-order Voronoi diagrams for colors in the plane, namely, the minimal and maximal order-k color Voronoi diagrams, which include various well-studied Voronoi diagrams as special cases. In this paper, we derive an exact upper bound 4k(n-k)-2n on the total number of vertices in both the minimal and maximal order-k color diagrams for a wide class of distance functions δ_s that satisfy certain conditions, including the case of point sites S under convex distance functions and the L_p metric for any 1 ≤ p ≤ ∞. For the L_1 (or, L_∞) metric, and other convex polygonal metrics, we show that the order-k minimal diagram of point sites has O(min{k(n-k), (n-k)²}) complexity, while its maximal counterpart has O(min{k(n-k), k²}) complexity. To obtain these combinatorial results, we extend the Clarkson-Shor framework to colored objects, and demonstrate its application to several fundamental geometric structures, including higher-order color Voronoi diagrams, colored j-facets, and levels in the arrangements of piecewise linear/algebraic curves/surfaces. We also present iterative algorithms to compute higher-order color Voronoi diagrams.
Cite as

Sang Won Bae, Nicolau Oliver, and Evanthia Papadopoulou. Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bae_et_al:LIPIcs.SoCG.2025.12,
  author =	{Bae, Sang Won and Oliver, Nicolau and Papadopoulou, Evanthia},
  title =	{{Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.12},
  URN =		{urn:nbn:de:0030-drops-231647},
  doi =		{10.4230/LIPIcs.SoCG.2025.12},
  annote =	{Keywords: higher-order Voronoi diagrams, color Voronoi diagrams, Hausdorff Voronoi diagrams, colored j-facets, arrangements, Clarkson-Shor technique}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2022.69
Subdivision Methods for Sum-Of-Distances Problems: Fermat-Weber Point, n-Ellipses and the Min-Sum Cluster Voronoi Diagram (Media Exposition)

Authors: Ioannis Mantas, Evanthia Papadopoulou, Martin Suderland, and Chee Yap

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Given a set P of n points, the sum of distances function of a point x is d_{P}(x) : = ∑_{p ∈ P} ||x - p||. Using a subdivision approach with soft predicates we implement and visualize approximate solutions for three different problems involving the sum of distances function in ℝ². Namely, (1) finding the Fermat-Weber point, (2) constructing n-ellipses of a given set of points, and (3) constructing the nearest Voronoi diagram under the sum of distances function, given a set of point clusters as sites.
Cite as

Ioannis Mantas, Evanthia Papadopoulou, Martin Suderland, and Chee Yap. Subdivision Methods for Sum-Of-Distances Problems: Fermat-Weber Point, n-Ellipses and the Min-Sum Cluster Voronoi Diagram (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 69:1-69:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mantas_et_al:LIPIcs.SoCG.2022.69,
  author =	{Mantas, Ioannis and Papadopoulou, Evanthia and Suderland, Martin and Yap, Chee},
  title =	{{Subdivision Methods for Sum-Of-Distances Problems: Fermat-Weber Point, n-Ellipses and the Min-Sum Cluster Voronoi Diagram}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{69:1--69:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.69},
  URN =		{urn:nbn:de:0030-drops-160773},
  doi =		{10.4230/LIPIcs.SoCG.2022.69},
  annote =	{Keywords: Fermat point, geometric median, Weber point, Fermat distance, sum of distances, n-ellipse, multifocal ellipse, min-sum Voronoi diagram, cluster Voronoi diagram}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.5
The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination

Authors: Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We introduce the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays, and the distance function is the counterclockwise angular distance between a point and a ray-site. This novel Voronoi diagram is motivated by illumination and coverage problems, where a domain has to be covered by floodlights (wedges) of uniform angle, and the goal is to find the minimum angle necessary to cover the domain. We study the diagram in the plane, and we present structural properties, combinatorial complexity bounds, and a construction algorithm. If the rays are induced by a convex polygon, we show how to construct the ray Voronoi diagram within this polygon in linear time. Using this information, we can find in optimal linear time the Brocard angle, the minimum angle required to illuminate a convex polygon with floodlights of uniform angle. This last algorithm improves upon previous results, settling an interesting open problem.
Cite as

Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland. The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alegria_et_al:LIPIcs.ESA.2021.5,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Papadopoulou, Evanthia and Savi\'{c}, Marko and Schrezenmaier, Hendrik and Seara, Carlos and Suderland, Martin},
  title =	{{The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.5},
  URN =		{urn:nbn:de:0030-drops-145865},
  doi =		{10.4230/LIPIcs.ESA.2021.5},
  annote =	{Keywords: rotating rays, Voronoi diagram, oriented angular distance, Brocard angle, floodlight illumination, coverage problems, art gallery problems}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.54
Certified Approximation Algorithms for the Fermat Point and n-Ellipses

Authors: Kolja Junginger, Ioannis Mantas, Evanthia Papadopoulou, Martin Suderland, and Chee Yap

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Given a set A of n points in ℝ^d with weight function w: A→ℝ_{> 0}, the Fermat distance function is φ(x): = ∑_{a∈A}w(a)‖x-a‖. A classic problem in facility location dating back to 1643, is to find the Fermat point x*, the point that minimizes the function φ. We consider the problem of computing a point x̃* that is an ε-approximation of x* in the sense that ‖x̃*-x*‖<ε. The algorithmic literature has so far used a different notion based on ε-approximation of the value φ(x*). We devise a certified subdivision algorithm for computing x̃*, enhanced by Newton operator techniques. We also revisit the classic Weiszfeld-Kuhn iteration scheme for x*, turning it into an ε-approximate Fermat point algorithm. Our second problem is the certified construction of ε-isotopic approximations of n-ellipses. These are the level sets φ^{-1}(r) for r > φ(x*) and d = 2. Finally, all our planar (d = 2) algorithms are implemented in order to experimentally evaluate them, using both synthetic as well as real world datasets. These experiments show the practicality of our techniques.
Cite as

Kolja Junginger, Ioannis Mantas, Evanthia Papadopoulou, Martin Suderland, and Chee Yap. Certified Approximation Algorithms for the Fermat Point and n-Ellipses. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 54:1-54:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{junginger_et_al:LIPIcs.ESA.2021.54,
  author =	{Junginger, Kolja and Mantas, Ioannis and Papadopoulou, Evanthia and Suderland, Martin and Yap, Chee},
  title =	{{Certified Approximation Algorithms for the Fermat Point and n-Ellipses}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{54:1--54:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.54},
  URN =		{urn:nbn:de:0030-drops-146359},
  doi =		{10.4230/LIPIcs.ESA.2021.54},
  annote =	{Keywords: Fermat point, n-ellipse, subdivision, approximation, certified, algorithms}
}
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