DROPS

Document

DOI: 10.4230/LIPIcs.ISAAC.2018.49

Competitive Searching for a Line on a Line Arrangement

Authors: Quirijn Bouts, Thom Castermans, Arthur van Goethem, Marc van Kreveld, and Wouter Meulemans

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract

We discuss the problem of searching for an unknown line on a known or unknown line arrangement by a searcher S, and show that a search strategy exists that finds the line competitively, that is, with detour factor at most a constant when compared to the situation where S has all knowledge. In the case where S knows all lines but not which one is sought, the strategy is 79-competitive. We also show that it may be necessary to travel on Omega(n) lines to realize a constant competitive ratio. In the case where initially, S does not know any line, but learns about the ones it encounters during the search, we give a 414.2-competitive search strategy.

Cite as

Quirijn Bouts, Thom Castermans, Arthur van Goethem, Marc van Kreveld, and Wouter Meulemans. Competitive Searching for a Line on a Line Arrangement. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 49:1-49:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{bouts_et_al:LIPIcs.ISAAC.2018.49,
  author =	{Bouts, Quirijn and Castermans, Thom and van Goethem, Arthur and van Kreveld, Marc and Meulemans, Wouter},
  title =	{{Competitive Searching for a Line on a Line Arrangement}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{49:1--49:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.49},
  URN =		{urn:nbn:de:0030-drops-99970},
  doi =		{10.4230/LIPIcs.ISAAC.2018.49},
  annote =	{Keywords: Competitive searching, line arrangement, detour factor, search strategy}
}

Document

Multimedia Contribution

DOI: 10.4230/LIPIcs.SoCG.2017.63

Ruler of the Plane - Games of Geometry (Multimedia Contribution)

Authors: Sander Beekhuis, Kevin Buchin, Thom Castermans, Thom Hurks, and Willem Sonke

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract

Ruler of the Plane is a set of games illustrating concepts from combinatorial and computational geometry. The games are based on the art gallery problem, ham-sandwich cuts, the Voronoi game, and geometric network connectivity problems like the Euclidean minimum spanning tree and traveling salesperson problem.

Cite as

Sander Beekhuis, Kevin Buchin, Thom Castermans, Thom Hurks, and Willem Sonke. Ruler of the Plane - Games of Geometry (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 63:1-63:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{beekhuis_et_al:LIPIcs.SoCG.2017.63,
  author =	{Beekhuis, Sander and Buchin, Kevin and Castermans, Thom and Hurks, Thom and Sonke, Willem},
  title =	{{Ruler of the Plane - Games of Geometry}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{63:1--63:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.63},
  URN =		{urn:nbn:de:0030-drops-72400},
  doi =		{10.4230/LIPIcs.SoCG.2017.63},
  annote =	{Keywords: art gallery problem, ham-sandwich cuts, Voronoi game, traveling sales-person problem}
}

Search Results

Documents authored by Castermans, Thom

Competitive Searching for a Line on a Line Arrangement

Abstract

Cite as

Ruler of the Plane - Games of Geometry (Multimedia Contribution)

Abstract

Cite as

Thanks for your feedback!

Could not send message