3 Search Results for "Knäuer, Simon"

Document
DOI: 10.4230/LIPIcs.ESA.2023.76
Improved Approximations for Translational Packing of Convex Polygons

Authors: Adam Kurpisz and Silvan Suter

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed. We study different settings depending on the type of containers used, including minimizing the number of containers or the size of the container based on an objective function. Building on prior research in the field, we develop polynomial-time algorithms with improved approximation guarantees upon the best-known results by Alt, de Berg and Knauer, as well as Aamand, Abrahamsen, Beretta and Kleist, for problems such as Polygon Area Minimization, Polygon Perimeter Minimization, Polygon Strip Packing, and Polygon Bin Packing. Our approach utilizes a sequence of object transformations that allows sorting by height and orientation, thus enhancing the effectiveness of shelf packing algorithms for polygon packing problems. In addition, we present efficient approximation algorithms for special cases of the Polygon Bin Packing problem, progressing toward solving an open question concerning an 𝒪(1)-approximation algorithm for arbitrary polygons.
Cite as

Adam Kurpisz and Silvan Suter. Improved Approximations for Translational Packing of Convex Polygons. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 76:1-76:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kurpisz_et_al:LIPIcs.ESA.2023.76,
  author =	{Kurpisz, Adam and Suter, Silvan},
  title =	{{Improved Approximations for Translational Packing of Convex Polygons}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{76:1--76:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.76},
  URN =		{urn:nbn:de:0030-drops-187299},
  doi =		{10.4230/LIPIcs.ESA.2023.76},
  annote =	{Keywords: Approximation algorithms, Packing problems, Convex polygons, Bin packing, Strip packing, Area minimization}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.116
Network Satisfaction Problems Solved by k-Consistency

Authors: Manuel Bodirsky and Simon Knäuer

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some k ∈ ℕ, is undecidable. For the important class of finite relation algebras A with a normal representation, however, the decidability of this problem remains open. We show that if A is symmetric and has a flexible atom, then the question whether NSP(A) can be solved by k-consistency, for some k ∈ ℕ, is decidable (even in polynomial time in the number of atoms of A). This result follows from a more general sufficient condition for the correctness of the k-consistency procedure for finite symmetric relation algebras. In our proof we make use of a result of Alexandr Kazda about finite binary conservative structures.
Cite as

Manuel Bodirsky and Simon Knäuer. Network Satisfaction Problems Solved by k-Consistency. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 116:1-116:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2023.116,
  author =	{Bodirsky, Manuel and Kn\"{a}uer, Simon},
  title =	{{Network Satisfaction Problems Solved by k-Consistency}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{116:1--116:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.116},
  URN =		{urn:nbn:de:0030-drops-181680},
  doi =		{10.4230/LIPIcs.ICALP.2023.116},
  annote =	{Keywords: Constraint Satisfaction, Computational Complexity, Relation Algebras, Network Satisfaction, Qualitative Reasoning, k-Consistency, Datalog}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.120
Datalog-Expressibility for Monadic and Guarded Second-Order Logic

Authors: Manuel Bodirsky, Simon Knäuer, and Sebastian Rudolph

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all 𝓁,k ∈ , there exists a canonical Datalog program Π of width (𝓁,k), that is, a Datalog program of width (𝓁,k) which is sound for C (i.e., Π only derives the goal predicate on a finite structure 𝔄 if 𝔄 ∈ C) and with the property that Π derives the goal predicate whenever some Datalog program of width (𝓁,k) which is sound for C derives the goal predicate. The same characterisations also hold for Guarded Second-order Logic (GSO), which properly extends MSO. To prove our results, we show that every class C in GSO whose complement is closed under homomorphisms is a finite union of constraint satisfaction problems (CSPs) of ω-categorical structures.
Cite as

Manuel Bodirsky, Simon Knäuer, and Sebastian Rudolph. Datalog-Expressibility for Monadic and Guarded Second-Order Logic. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 120:1-120:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2021.120,
  author =	{Bodirsky, Manuel and Kn\"{a}uer, Simon and Rudolph, Sebastian},
  title =	{{Datalog-Expressibility for Monadic and Guarded Second-Order Logic}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{120:1--120:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.120},
  URN =		{urn:nbn:de:0030-drops-141897},
  doi =		{10.4230/LIPIcs.ICALP.2021.120},
  annote =	{Keywords: Monadic Second-order Logic, Guarded Second-order Logic, Datalog, constraint satisfaction, homomorphism-closed, conjunctive query, primitive positive formula, pebble game, \omega-categoricity}
}
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