2 Search Results for "Kamphans, Tom"

Document
DOI: 10.4230/LIPIcs.STACS.2026.54
A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm

Authors: Stefan Hougardy and Bart Zondervan

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis‑parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the height of the packing. This problem is known to be NP-hard. The Bottom-Left Algorithm is a simple and widely used heuristic for Strip Packing. Given a fixed order of the rectangles, it places them one by one, always choosing the lowest feasible position in the strip and, in case of ties, the leftmost one. Baker, Coffman, and Rivest proved in 1980 that the Bottom-Left Algorithm has approximation ratio 3 if the rectangles are sorted by decreasing width [Brenda S. Baker et al., 1980]. For the past 45 years, no alternative ordering has been found that improves this bound. We introduce a new rectangle ordering and show that with this ordering the Bottom-Left Algorithm achieves a 13/6 approximation for the Strip Packing problem.
Cite as

Stefan Hougardy and Bart Zondervan. A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{hougardy_et_al:LIPIcs.STACS.2026.54,
  author =	{Hougardy, Stefan and Zondervan, Bart},
  title =	{{A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.54},
  URN =		{urn:nbn:de:0030-drops-255432},
  doi =		{10.4230/LIPIcs.STACS.2026.54},
  annote =	{Keywords: Approximation Algorithm, Strip Packing, Bottom-Left Algorithm, Rectangle Packing}
}
Document
DOI: 10.4230/DagSemProc.06421.5
Competitive Online Searching for a Ray in the Plane

Authors: Andrea Eubeler, Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, and Gerhard Trippen

Published in: Dagstuhl Seminar Proceedings, Volume 6421, Robot Navigation (2007)

Abstract
We consider the problem of a searcher that looks, for example, for a lost flashlight in a dusty environment. The searcher finds the flashlight as soon as it crosses the ray emanating from the flashlight. In order to pick it up, the searcher moves to the origin of the light beam. We compare the length of the path of the searcher to the shortest path to the goal. First, we give a search strategy for a special case of the ray search---the window shopper problem---, where the ray we are looking for is perpendicular to a known ray. Our strategy achieves a competitive factor of $1.059ldots$, which is optimal. Then, we consider rays in arbitrary position in the plane. We present an online strategy that achieves a factor of $22.513ldots$, and give a lower bound of $2pi,e=17.079ldots$.
Cite as

Andrea Eubeler, Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, and Gerhard Trippen. Competitive Online Searching for a Ray in the Plane. In Robot Navigation. Dagstuhl Seminar Proceedings, Volume 6421, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

Copy BibTex To Clipboard

@InProceedings{eubeler_et_al:DagSemProc.06421.5,
  author =	{Eubeler, Andrea and Fleischer, Rudolf and Kamphans, Tom and Klein, Rolf and Langetepe, Elmar and Trippen, Gerhard},
  title =	{{Competitive Online Searching for a Ray in the Plane}},
  booktitle =	{Robot Navigation},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6421},
  editor =	{S\'{a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06421.5},
  URN =		{urn:nbn:de:0030-drops-8687},
  doi =		{10.4230/DagSemProc.06421.5},
  annote =	{Keywords: Online motion planning, competitive analysis, ray search}
}
  • Refine by Type
  • 2 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 1 2007

  • Refine by Author
  • 1 Eubeler, Andrea
  • 1 Fleischer, Rudolf
  • 1 Hougardy, Stefan
  • 1 Kamphans, Tom
  • 1 Klein, Rolf
  • Show More...

  • Refine by Series/Journal
  • 1 LIPIcs
  • 1 DagSemProc

  • Refine by Classification
  • 1 Theory of computation → Packing and covering problems

  • Refine by Keyword
  • 1 Approximation Algorithm
  • 1 Bottom-Left Algorithm
  • 1 Online motion planning
  • 1 Rectangle Packing
  • 1 Strip Packing
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact