2 Search Results for "Ackerman, Eyal"


Document
An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons

Authors: Eyal Ackerman, Balázs Keszegh, and Günter Rote

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
What is the maximum number of intersections of the boundaries of a simple m-gon and a simple n-gon, assuming general position? This is a basic question in combinatorial geometry, and the answer is easy if at least one of m and n is even. If both m and n are odd, the best known construction has mn-(m+n)+3 intersections, and it is conjectured that this is the maximum. However, the best known upper bound is only mn-(m + ⌈ n/6 ⌉), for m ≥ n. We prove a new upper bound of mn-(m+n)+C for some constant C, which is optimal apart from the value of C.

Cite as

Eyal Ackerman, Balázs Keszegh, and Günter Rote. An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ackerman_et_al:LIPIcs.SoCG.2020.1,
  author =	{Ackerman, Eyal and Keszegh, Bal\'{a}zs and Rote, G\"{u}nter},
  title =	{{An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.1},
  URN =		{urn:nbn:de:0030-drops-121591},
  doi =		{10.4230/LIPIcs.SoCG.2020.1},
  annote =	{Keywords: Simple polygon, Ramsey theory, combinatorial geometry}
}
Document
Coloring Points with Respect to Squares

Authors: Eyal Ackerman, Balázs Keszegh, and Máté Vizer

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)


Abstract
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a constant m such that any finite set S of points in the plane can be 2-colored such that every axis-parallel square that contains at least m points from S contains points of both colors. Our proof is constructive, that is, it provides a polynomial-time algorithm for obtaining such a 2-coloring. By affine transformations this result immediately applies also when considering homothets of a fixed parallelogram.

Cite as

Eyal Ackerman, Balázs Keszegh, and Máté Vizer. Coloring Points with Respect to Squares. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{ackerman_et_al:LIPIcs.SoCG.2016.5,
  author =	{Ackerman, Eyal and Keszegh, Bal\'{a}zs and Vizer, M\'{a}t\'{e}},
  title =	{{Coloring Points with Respect to Squares}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.5},
  URN =		{urn:nbn:de:0030-drops-58972},
  doi =		{10.4230/LIPIcs.SoCG.2016.5},
  annote =	{Keywords: Geometric hypergraph coloring, Polychromatic coloring, Homothets, Cover-decomposability}
}
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