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Documents authored by Orgo, Ly

Document
DOI: 10.4230/LIPIcs.GD.2025.21
On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

Authors: Parinya Chalermsook, Ly Orgo, and Minoo Zarsav

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.
Cite as

Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
  author =	{Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
  title =	{{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.21},
  URN =		{urn:nbn:de:0030-drops-250074},
  doi =		{10.4230/LIPIcs.GD.2025.21},
  annote =	{Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.16
An Improved Guillotine Cut for Squares

Authors: Parinya Chalermsook, Axel Kugelmann, Ly Orgo, Sumedha Uniyal, and Minoo Zarsav

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

Abstract
Given a set of n non-overlapping geometric objects, can we separate a constant fraction of them using straight-line cuts that extend from edge to edge? In 1996, Urrutia posed this question for compact convex objects. Pach and Tardos later refuted it for general line segments by constructing a family where any separable subfamily has size at most O (n^{log₃ 2}). However, for axis-parallel rectangles, they provided positive evidence, showing that an Ω(1/log n)-fraction can be separated. This problem naturally arises in geometric approximation algorithms. In particular, when restricting cuts to only orthogonal straight lines, known as a guillotine cut sequence, any bound on the separability ratio directly translates into a clean and simple dynamic programming for computing a maximum independent set of geometric objects. This paper focuses on the case when the objects are squares. For squares of arbitrary sizes, an Ω(1)-fraction can be separated (Abed et al., APPROX 2015), recently improved to 1/40 (and 1/160 ≈ 0.62% for the weighted case) (Khan and Pittu, APPROX 2020). We further improve this bound, showing that a 9/256 ≈ 3.51% can be separated for the weighted case. This result significantly narrows the possible range for squares to [3.51%, 50%]. The key to our improvement is a refined analysis of the existing framework.
Cite as

Parinya Chalermsook, Axel Kugelmann, Ly Orgo, Sumedha Uniyal, and Minoo Zarsav. An Improved Guillotine Cut for Squares. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chalermsook_et_al:LIPIcs.WADS.2025.16,
  author =	{Chalermsook, Parinya and Kugelmann, Axel and Orgo, Ly and Uniyal, Sumedha and Zarsav, Minoo},
  title =	{{An Improved Guillotine Cut for Squares}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{16:1--16:19},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-242472},
  doi =		{10.4230/LIPIcs.WADS.2025.16},
  annote =	{Keywords: Guillotine cuts, Geometric Approximation Algorithms, Rectangles, Squares}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.33
Polynomial-Time Approximation of Independent Set Parameterized by Treewidth

Authors: Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo

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

Abstract
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a "non-trivial" approximation ratio (as a function of the number of vertices of the input graph G) can be turned into an approximation algorithm achieving almost the same ratio, albeit as a function of the treewidth of G. More formally, we prove that for any function f, the existence of a polynomial time (n/f(n))-approximation algorithm yields the existence of a polynomial time O(tw⋅log{f(tw)}/f(tw))-approximation algorithm, where n and tw denote the number of vertices and the width of a given tree decomposition of the input graph. By pipelining our result with the state-of-the-art O(n ⋅ (log log n)²/log³n)-approximation algorithm by Feige (2004), this implies an O(tw⋅(log log tw)³/log³tw)-approximation algorithm.
Cite as

Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo. Polynomial-Time Approximation of Independent Set Parameterized by Treewidth. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 33:1-33:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chalermsook_et_al:LIPIcs.ESA.2023.33,
  author =	{Chalermsook, Parinya and Fomin, Fedor and Hamm, Thekla and Korhonen, Tuukka and Nederlof, Jesper and Orgo, Ly},
  title =	{{Polynomial-Time Approximation of Independent Set Parameterized by Treewidth}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{33:1--33:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.33},
  URN =		{urn:nbn:de:0030-drops-186865},
  doi =		{10.4230/LIPIcs.ESA.2023.33},
  annote =	{Keywords: Maximum Independent Set, Treewidth, Approximation Algorithms, Parameterized Approximation}
}
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