9 Search Results for "An, Shinwoo"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.36
Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates

Authors: Seongbin Park and Eunjin Oh

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets R,B ⊂ [Δ]² with |R|+|B| = n, the goal is to select a set of edges between R and B so that every point is incident to at least one edge and the total Euclidean length is minimized. In the general case that R and B are point sets in the plane, the best-known algorithm for the many-to-many matching problem takes Õ(n²) time. We present an exact Õ(n^{1.5} log Δ) time algorithm for point sets in [Δ]². To the best of our knowledge, this is the first subquadratic exact algorithm for planar many-to-many matching under bounded integer coordinates.
Cite as

Seongbin Park and Eunjin Oh. Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{park_et_al:LIPIcs.SWAT.2026.36,
  author =	{Park, Seongbin and Oh, Eunjin},
  title =	{{Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36},
  URN =		{urn:nbn:de:0030-drops-260728},
  doi =		{10.4230/LIPIcs.SWAT.2026.36},
  annote =	{Keywords: Edge cover, many-to-many matching, similarity, geometric matching}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.18
Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs

Authors: Thomas Bläsius, Emil Dohse, Deborah Haun, and Laura Merker

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Hyperbolic uniform disk graphs (HUDGs) are intersection graphs of disks with some radius r in the hyperbolic plane, where r may be constant or depend on the number of vertices in a family of HUDGs. We show that HUDGs with constant clique number do not admit product structure, i.e., that there is no constant c such that every such graph is a subgraph of H ⊠ P for some graph H of treewidth at most c. This justifies that HUDGs are described as not having a grid-like structure in the literature, and is in contrast to unit disk graphs in the Euclidean plane, whose grid-like structure is evident from the fact that they are subgraphs of the strong product of two paths and a clique of constant size [Dvořák et al., '21, MATRIX Annals]. By allowing H to be any graph of constant treewidth instead of a path-like graph, we reject the possibility of a grid-like structure not merely by the maximum degree (which is unbounded for HUDGs) but due to their global structure. We complement this by showing that for every (sub-)constant r, HUDGs admit product structure, whereas the typical hyperbolic behavior is observed if r grows with the number of vertices. Our proof involves a family of n-vertex HUDGs with radius log n that has bounded clique number but unbounded treewidth, and one for which the ratio of treewidth and clique number is log n / log log n. Up to a log log n factor, this negatively answers a question raised by Bläsius et al. [SoCG '25] asking whether balanced separators of HUDGs with radius log n can be covered by less than log n cliques. Our results also imply that the local and layered tree-independence number of HUDGs are both unbounded, answering an open question of Dallard et al. [arXiv '25].
Cite as

Thomas Bläsius, Emil Dohse, Deborah Haun, and Laura Merker. Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blasius_et_al:LIPIcs.SoCG.2026.18,
  author =	{Bl\"{a}sius, Thomas and Dohse, Emil and Haun, Deborah and Merker, Laura},
  title =	{{Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.18},
  URN =		{urn:nbn:de:0030-drops-258249},
  doi =		{10.4230/LIPIcs.SoCG.2026.18},
  annote =	{Keywords: hyperbolic uniform disk graphs, product structure, treewidth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.31
An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs

Authors: Bruce W. Brewer and Haitao Wang

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Given in the plane a set S of n points and a set of disks centered at these points, the disk graph G(S) induced by these disks has vertex set S and an edge between two vertices if their disks intersect. Note that the disks may have different radii. We consider the problem of computing shortest paths from a source point s ∈ S to all vertices in G(S) where the length of a path in G(S) is defined as the number of edges in the path. The previously best algorithm solves the problem in O(nlog² n) time. A lower bound of Ω(nlog n) is also known for this problem under the algebraic decision tree model. In this paper, we present an O(nlog n) time algorithm, which matches the lower bound and thus is optimal. Another virtue of our algorithm is that it is quite simple.
Cite as

Bruce W. Brewer and Haitao Wang. An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 31:1-31:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brewer_et_al:LIPIcs.ESA.2025.31,
  author =	{Brewer, Bruce W. and Wang, Haitao},
  title =	{{An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{31:1--31:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.31},
  URN =		{urn:nbn:de:0030-drops-244997},
  doi =		{10.4230/LIPIcs.ESA.2025.31},
  annote =	{Keywords: disk graphs, weighted Voronoi diagrams, shortest paths}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.26
Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set

Authors: Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph G and a parameter k, one has to decide if there is a set S of at most k vertices such that G-S is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time 2^{o(k)}n^{𝒪(1)} in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such 2^{o(k)}n^{𝒪(1)} algorithms. In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time 2^k^ε poly(n), for some ε < 1, where n denotes the number of vertices of the instance and k the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of "thin" objects like segment graphs or more generally s-string graphs.
Cite as

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berthe_et_al:LIPIcs.ICALP.2025.26,
  author =	{Berthe, Ga\'{e}tan and Bougeret, Marin and Gon\c{c}alves, Daniel and Raymond, Jean-Florent},
  title =	{{Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.26},
  URN =		{urn:nbn:de:0030-drops-234036},
  doi =		{10.4230/LIPIcs.ICALP.2025.26},
  annote =	{Keywords: Subexponential FPT algorithms, geometric intersection graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.7
Single-Source Shortest Path Problem in Weighted Disk Graphs

Authors: Shinwoo An, Eunjin Oh, and Jie Xue

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

Abstract
In this paper, we present efficient algorithms for the single-source shortest path problem in weighted disk graphs. A disk graph is the intersection graph of a family of disks in the plane. Here, the weight of an edge is defined as the Euclidean distance between the centers of the disks corresponding to the endpoints of the edge. Given a family of n disks in the plane whose radii lie in [1,Ψ] and a source disk, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog² n log Ψ) time. Moreover, in the case that the radii of disks are arbitrarily large, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog⁴ n) time. This improves the best-known algorithm running in O(nlog⁶ n) time presented in ESA'23.
Cite as

Shinwoo An, Eunjin Oh, and Jie Xue. Single-Source Shortest Path Problem in Weighted Disk Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{an_et_al:LIPIcs.SoCG.2025.7,
  author =	{An, Shinwoo and Oh, Eunjin and Xue, Jie},
  title =	{{Single-Source Shortest Path Problem in Weighted Disk Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{7:1--7:15},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-231594},
  doi =		{10.4230/LIPIcs.SoCG.2025.7},
  annote =	{Keywords: Disk graphs, shortest path problem, compressed quadtrees}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.6
Dynamic Parameterized Problems on Unit Disk Graphs

Authors: Shinwoo An, Kyungjin Cho, Leo Jang, Byeonghyeon Jung, Yudam Lee, Eunjin Oh, Donghun Shin, Hyeonjun Shin, and Chanho Song

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
In this paper, we study fundamental parameterized problems such as k-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set V changing dynamically under vertex insertions and deletions, our goal is to maintain data structures so that the aforementioned parameterized problems on the unit disk graph induced by V can be solved efficiently. Although dynamic parameterized problems on general graphs have been studied extensively, no previous work focuses on unit disk graphs. In this paper, we present the first data structures for fundamental parameterized problems on dynamic unit disk graphs. More specifically, our data structure supports 2^O(√k) update time and O(k) query time for k-Path/Cycle. For the other problems, our data structures support O(log n) update time and 2^O(√k) query time, where k denotes the output size.
Cite as

Shinwoo An, Kyungjin Cho, Leo Jang, Byeonghyeon Jung, Yudam Lee, Eunjin Oh, Donghun Shin, Hyeonjun Shin, and Chanho Song. Dynamic Parameterized Problems on Unit Disk Graphs. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{an_et_al:LIPIcs.ISAAC.2024.6,
  author =	{An, Shinwoo and Cho, Kyungjin and Jang, Leo and Jung, Byeonghyeon and Lee, Yudam and Oh, Eunjin and Shin, Donghun and Shin, Hyeonjun and Song, Chanho},
  title =	{{Dynamic Parameterized Problems on Unit Disk Graphs}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.6},
  URN =		{urn:nbn:de:0030-drops-221337},
  doi =		{10.4230/LIPIcs.ISAAC.2024.6},
  annote =	{Keywords: Unit disk graphs, dynamic parameterized algorithms, kernelization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.10
Sparse Outerstring Graphs Have Logarithmic Treewidth

Authors: Shinwoo An, Eunjin Oh, and Jie Xue

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
An outerstring graph is the intersection graph of curves lying inside a disk with one endpoint on the boundary of the disk. We show that an outerstring graph with n vertices has treewidth O(αlog n), where α denotes the arboricity of the graph, with an almost matching lower bound of Ω(α log (n/α)). As a corollary, we show that a t-biclique-free outerstring graph has treewidth O(t(log t)log n). This leads to polynomial-time algorithms for most of the central NP-complete problems such as Independent Set, Vertex Cover, Dominating Set, Feedback Vertex Set, Coloring for sparse outerstring graphs. Also, we can obtain subexponential-time (exact, parameterized, and approximation) algorithms for various NP-complete problems such as Vertex Cover, Feedback Vertex Set and Cycle Packing for (not necessarily sparse) outerstring graphs.
Cite as

Shinwoo An, Eunjin Oh, and Jie Xue. Sparse Outerstring Graphs Have Logarithmic Treewidth. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{an_et_al:LIPIcs.ESA.2024.10,
  author =	{An, Shinwoo and Oh, Eunjin and Xue, Jie},
  title =	{{Sparse Outerstring Graphs Have Logarithmic Treewidth}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.10},
  URN =		{urn:nbn:de:0030-drops-210816},
  doi =		{10.4230/LIPIcs.ESA.2024.10},
  annote =	{Keywords: Outerstring graphs, geometric intersection graphs, treewidth}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.7
ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs

Authors: Shinwoo An and Eunjin Oh

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
In this paper, we consider the Cycle Packing problem on a unit disk graph defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of k vertex-disjoint cycles of G if it exists. Our algorithm runs in time 2^O(√k) n^O(1). This improves the 2^O(√klog k) n^O(1)-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.
Cite as

Shinwoo An and Eunjin Oh. ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{an_et_al:LIPIcs.SoCG.2024.7,
  author =	{An, Shinwoo and Oh, Eunjin},
  title =	{{ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.7},
  URN =		{urn:nbn:de:0030-drops-199522},
  doi =		{10.4230/LIPIcs.SoCG.2024.7},
  annote =	{Keywords: Unit disk graphs, cycle packing, tree decomposition, parameterized algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.47
Feedback Vertex Set on Geometric Intersection Graphs

Authors: Shinwoo An and Eunjin Oh

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time 2^O(√k)(n+m), where n and m denote the numbers of vertices and edges, respectively. This improves the 2^O(√klog k) n^O(1)-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis. Also, our algorithm can be extended to handle geometric intersection graphs of similarly sized fat objects without increasing the running time.
Cite as

Shinwoo An and Eunjin Oh. Feedback Vertex Set on Geometric Intersection Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 47:1-47:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{an_et_al:LIPIcs.ISAAC.2021.47,
  author =	{An, Shinwoo and Oh, Eunjin},
  title =	{{Feedback Vertex Set on Geometric Intersection Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{47:1--47:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.47},
  URN =		{urn:nbn:de:0030-drops-154807},
  doi =		{10.4230/LIPIcs.ISAAC.2021.47},
  annote =	{Keywords: Feedback vertex set, intersection graphs, parameterized algorithm}
}
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