6 Search Results for "Pór, Attila"

Document
DOI: 10.4230/LIPIcs.WADS.2025.29
Linear Layouts of Graphs with Priority Queues

Authors: Emilio Di Giacomo, Walter Didimo, Henry Förster, Torsten Ueckerdt, and Johannes Zink

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear layouts are stack and queue layouts, in which any two edges assigned to the same page are forbidden to cross and nest, respectively. The names of these two layouts derive from the fact that, when parsing the graph according to the linear vertex ordering, the edges in a single page can be stored using a single stack or queue, respectively. Recently, the concepts of stack and queue layouts have been extended by using a double-ended queue or a restricted-input queue for storing the edges of a page. We extend this line of study to edge-weighted graphs by introducing priority queue layouts, that is, the edges on each page are stored in a priority queue whose keys are the edge weights. First, we show that there are edge-weighted graphs that require a linear number of priority queues. Second, we characterize the graphs that admit a priority queue layout with a single queue, regardless of the edge-weight function, and we provide an efficient recognition algorithm. Third, we show that the number of priority queues required independently of the edge-weight function is bounded by the pathwidth of the graph, but can be arbitrarily large already for graphs of treewidth two. Finally, we prove that determining the minimum number of priority queues is NP-complete if the linear ordering of the vertices is fixed.
Cite as

Emilio Di Giacomo, Walter Didimo, Henry Förster, Torsten Ueckerdt, and Johannes Zink. Linear Layouts of Graphs with Priority Queues. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{digiacomo_et_al:LIPIcs.WADS.2025.29,
  author =	{Di Giacomo, Emilio and Didimo, Walter and F\"{o}rster, Henry and Ueckerdt, Torsten and Zink, Johannes},
  title =	{{Linear Layouts of Graphs with Priority Queues}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.29},
  URN =		{urn:nbn:de:0030-drops-242602},
  doi =		{10.4230/LIPIcs.WADS.2025.29},
  annote =	{Keywords: linear layouts, recognition and characterization, priority queue layouts}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.61
k-Dimensional Transversals for Fat Convex Sets

Authors: Attila Jung and Dömötör Pálvölgyi

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

Abstract
We prove a fractional Helly theorem for k-flats intersecting fat convex sets. A family ℱ of sets is said to be ρ-fat if every set in the family contains a ball and is contained in a ball such that the ratio of the radii of these balls is bounded by ρ. We prove that for every dimension d and positive reals ρ and α there exists a positive β = β(d,ρ, α) such that if ℱ is a finite family of ρ-fat convex sets in ℝ^d and an α-fraction of the (k+2)-size subfamilies from ℱ can be hit by a k-flat, then there is a k-flat that intersects at least a β-fraction of the sets of ℱ. We prove spherical and colorful variants of the above results and prove a (p,k+2)-theorem for k-flats intersecting balls.
Cite as

Attila Jung and Dömötör Pálvölgyi. k-Dimensional Transversals for Fat Convex Sets. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jung_et_al:LIPIcs.SoCG.2025.61,
  author =	{Jung, Attila and P\'{a}lv\"{o}lgyi, D\"{o}m\"{o}t\"{o}r},
  title =	{{k-Dimensional Transversals for Fat Convex Sets}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{61:1--61:12},
  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.2025.61},
  URN =		{urn:nbn:de:0030-drops-232136},
  doi =		{10.4230/LIPIcs.SoCG.2025.61},
  annote =	{Keywords: discrete geometry, transversals, Helly, hypergraphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.45
Forbidden Patterns in Mixed Linear Layouts

Authors: Deborah Haun, Laura Merker, and Sergey Pupyrev

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue) number of an ordered graph is the minimum number of required stacks (queues). Mixed linear layouts combine these layouts by allowing each set of edges to form either a stack or a queue. The minimum number of stacks plus queues is called the mixed page number. It is well known that ordered graphs with small stack number are characterized, up to a function, by the absence of large twists (that is, pairwise crossing edges). Similarly, ordered graphs with small queue number are characterized by the absence of large rainbows (that is, pairwise nesting edges). However, no such characterization via forbidden patterns is known for mixed linear layouts. We address this gap by introducing patterns similar to twists and rainbows, which we call thick patterns; such patterns allow a characterization, again up to a function, of mixed linear layouts of bounded-degree graphs. That is, we show that a family of ordered graphs with bounded maximum degree has bounded mixed page number if and only if the size of the largest thick pattern is bounded. In addition, we investigate an exact characterization of ordered graphs whose mixed page number equals a fixed integer k via a finite set of forbidden patterns. We show that for k = 2, there is no such characterization, which supports the nature of our first result.
Cite as

Deborah Haun, Laura Merker, and Sergey Pupyrev. Forbidden Patterns in Mixed Linear Layouts. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haun_et_al:LIPIcs.STACS.2025.45,
  author =	{Haun, Deborah and Merker, Laura and Pupyrev, Sergey},
  title =	{{Forbidden Patterns in Mixed Linear Layouts}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{45:1--45:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.45},
  URN =		{urn:nbn:de:0030-drops-228717},
  doi =		{10.4230/LIPIcs.STACS.2025.45},
  annote =	{Keywords: Ordered Graphs, linear Layout, mixed linear Layout, Stack Layout, Queue Layout}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.56
Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs

Authors: Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Some of the most important open problems for linear layouts of graphs ask for the relation between a graph’s queue number and its stack number or mixed number. In such, we seek a vertex order and edge partition of G into parts with pairwise non-crossing edges (a stack) or with pairwise non-nesting edges (a queue). Allowing only stacks, only queues, or both, the minimum number of required parts is the graph’s stack number sn(G), queue number qn(G), and mixed number mn(G), respectively. Already in 1992, Heath and Rosenberg asked whether qn(G) is bounded in terms of sn(G), that is, whether stacks "can be transformed into" queues. This is equivalent to bipartite 3-stack graphs having bounded queue number (Dujmović and Wood, 2005). Recently, Alam et al. asked whether qn(G) is bounded in terms of mn(G), which we show to also be equivalent to the previous questions. We approach the problem by considering separated linear layouts of bipartite graphs. In this natural setting all vertices of one part must precede all vertices of the other part. Separated stack and queue numbers coincide, and for fixed vertex orders, graphs with bounded separated stack/queue number can be characterized and efficiently recognized, whereas the separated mixed layouts are more challenging. In this work, we thoroughly investigate the relationship between separated and non-separated, mixed and pure linear layouts.
Cite as

Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt. Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{katheder_et_al:LIPIcs.STACS.2025.56,
  author =	{Katheder, Julia and Kaufmann, Michael and Pupyrev, Sergey and Ueckerdt, Torsten},
  title =	{{Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{56:1--56:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.56},
  URN =		{urn:nbn:de:0030-drops-228819},
  doi =		{10.4230/LIPIcs.STACS.2025.56},
  annote =	{Keywords: Separated linear Layouts, Stack Number, Queue Number, mixed Number, bipartite Graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.14
Orientation Preserving Maps of the Square Grid

Authors: Imre Bárány, Attila Pór, and Pavel Valtr

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
For a finite set A ⊂ ℝ², a map φ: A → ℝ² is orientation preserving if for every non-collinear triple u,v,w ∈ A the orientation of the triangle u,v,w is the same as that of the triangle φ(u),φ(v),φ(w). We prove that for every n ∈ ℕ and for every ε > 0 there is N = N(n,ε) ∈ ℕ such that the following holds. Assume that φ:G(N) → ℝ² is an orientation preserving map where G(N) is the grid {(i,j) ∈ ℤ²: -N ≤ i,j ≤ N}. Then there is an affine transformation ψ :ℝ² → ℝ² and a ∈ ℤ² such that a+G(n) ⊂ G(N) and ‖ψ∘φ (z)-z‖ < ε for every z ∈ a+G(n). This result was previously proved in a completely different way by Nešetřil and Valtr, without obtaining any bound on N. Our proof gives N(n,ε) = O(n⁴ε^{-2}).
Cite as

Imre Bárány, Attila Pór, and Pavel Valtr. Orientation Preserving Maps of the Square Grid. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{barany_et_al:LIPIcs.SoCG.2021.14,
  author =	{B\'{a}r\'{a}ny, Imre and P\'{o}r, Attila and Valtr, Pavel},
  title =	{{Orientation Preserving Maps of the Square Grid}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{14:1--14:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.14},
  URN =		{urn:nbn:de:0030-drops-138130},
  doi =		{10.4230/LIPIcs.SoCG.2021.14},
  annote =	{Keywords: square grid, plane, order type}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.69
Double Threshold Digraphs

Authors: Peter Hamburger, Ross M. McConnell, Attila Pór, Jeremy P. Spinrad, and Zhisheng Xu

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
A semiorder is a model of preference relations where each element x is associated with a utility value alpha(x), and there is a threshold t such that y is preferred to x iff alpha(y) - alpha(x) > t. These are motivated by the notion that there is some uncertainty in the utility values we assign an object or that a subject may be unable to distinguish a preference between objects whose values are close. However, they fail to model the well-known phenomenon that preferences are not always transitive. Also, if we are uncertain of the utility values, it is not logical that preference is determined absolutely by a comparison of them with an exact threshold. We propose a new model in which there are two thresholds, t_1 and t_2; if the difference alpha(y) - alpha(x) is less than t_1, then y is not preferred to x; if the difference is greater than t_2 then y is preferred to x; if it is between t_1 and t_2, then y may or may not be preferred to x. We call such a relation a (t_1,t_2) double-threshold semiorder, and the corresponding directed graph G = (V,E) a (t_1,t_2) double-threshold digraph. Every directed acyclic graph is a double-threshold digraph; increasing bounds on t_2/t_1 give a nested hierarchy of subclasses of the directed acyclic graphs. In this paper we characterize the subclasses in terms of forbidden subgraphs, and give algorithms for finding an assignment of utility values that explains the relation in terms of a given (t_1,t_2) or else produces a forbidden subgraph, and finding the minimum value lambda of t_2/t_1 that is satisfiable for a given directed acyclic graph. We show that lambda gives a useful measure of the complexity of a directed acyclic graph with respect to several optimization problems that are NP-hard on arbitrary directed acyclic graphs.
Cite as

Peter Hamburger, Ross M. McConnell, Attila Pór, Jeremy P. Spinrad, and Zhisheng Xu. Double Threshold Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 69:1-69:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hamburger_et_al:LIPIcs.MFCS.2018.69,
  author =	{Hamburger, Peter and McConnell, Ross M. and P\'{o}r, Attila and Spinrad, Jeremy P. and Xu, Zhisheng},
  title =	{{Double Threshold Digraphs}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{69:1--69:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.69},
  URN =		{urn:nbn:de:0030-drops-96519},
  doi =		{10.4230/LIPIcs.MFCS.2018.69},
  annote =	{Keywords: posets, preference relations, approximation algorithms}
}
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