93 Search Results for "Oh, Eunjin"

Volume

LIPIcs, Volume 349

19th International Symposium on Algorithms and Data Structures (WADS 2025)

WADS 2025, August 11-15, 2025, York University, Toronto, Canada

Editors: Pat Morin and Eunjin Oh

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.33
Visibility Queries in Simple Polygons

Authors: Sujoy Bhore, Chih-Hung Liu, Anurag Murty Naredla, Yakov Nekrich, Eunjin Oh, André van Renssen, Frank Staals, Haitao Wang, and Jie Xue

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Given a simple polygon P with n vertices, we consider the problem of constructing a data structure for visibility queries: for any query point q ∈ P, compute the visibility polygon of q in P. To obtain O(log n + k) query time, where k is the size of the visibility polygon of q, the previous best result requires O(n³) space. In this paper, we propose a new data structure that uses O(n^{2+ε}) space, for any ε > 0, while achieving the same query time. If only O(n²) space is available, the best known result provides O(log² n + k) query time. We improve this to O(log n log log n + k) time. When restricted to o(n²) space, the only previously known approach, aside from the O(n)-time algorithm that computes the visibility polygon without preprocessing, is an O(n)-space data structure that supports O(k log n)-time queries. We construct a data structure using O(n log n) space that answers visibility queries in O(n^{1/2+ε} + k) time. In addition, for the special case in which q lies on the boundary of P, we build a data structure of O(n log n) space supporting O(log² n + k) query time; alternatively, we achieve O(log n + k) query time using O(n^{1+ε}) space. To achieve our results, we propose a new method for decomposing simple polygons, which may be of independent interest.
Cite as

Sujoy Bhore, Chih-Hung Liu, Anurag Murty Naredla, Yakov Nekrich, Eunjin Oh, André van Renssen, Frank Staals, Haitao Wang, and Jie Xue. Visibility Queries in Simple Polygons. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bhore_et_al:LIPIcs.ICALP.2026.33,
  author =	{Bhore, Sujoy and Liu, Chih-Hung and Naredla, Anurag Murty and Nekrich, Yakov and Oh, Eunjin and van Renssen, Andr\'{e} and Staals, Frank and Wang, Haitao and Xue, Jie},
  title =	{{Visibility Queries in Simple Polygons}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.33},
  URN =		{urn:nbn:de:0030-drops-264222},
  doi =		{10.4230/LIPIcs.ICALP.2026.33},
  annote =	{Keywords: simple polygons, visibility polygons, visibility queries, polygon decompositions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.50
Touring a Sequence of Orthogonal Polygons

Authors: Katrin Casel, Sándor Kisfaludi-Bak, Linda Kleist, Jeroen S.K. Lamme, Eunjin Oh, and Yanheng Wang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We study the problem of computing a shortest tour that visits a sequence of k polygons P₁,…,P_k with a total number of n vertices. A tour is an oriented curve such that there exist points p_i ∈ P_i for all i where p_i appears not after p_{i+1}. In a seminal paper, Dror, Efrat, Lubiw and Mitchell (STOC 2003) considered the problem under L₂ distance, and gave Õ(nk) and Õ(nk²) algorithms for disjoint and intersecting convex polygons, respectively. In this paper, we consider the orthogonal setting (with orthogonal polygons and Manhattan distance) and obtain the following results: - a truly subquadratic Õ(n^{2-1/48}) algorithm when consecutive polygons in the sequence are disjoint; - an Õ(n) algorithm for ortho-convex polygons when consecutive polygons are disjoint; - an O(n) algorithm for axis-aligned rectangles; - Õ(n²) and Õ(n^{1.5}k²) algorithms without restrictions. Our algorithms build on a wide range of techniques, including additively weighted Voronoi diagrams, rectangle decompositions, persistent data structures, and dynamic distance oracles for weighted planar graphs.
Cite as

Katrin Casel, Sándor Kisfaludi-Bak, Linda Kleist, Jeroen S.K. Lamme, Eunjin Oh, and Yanheng Wang. Touring a Sequence of Orthogonal Polygons. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 50:1-50:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{casel_et_al:LIPIcs.ICALP.2026.50,
  author =	{Casel, Katrin and Kisfaludi-Bak, S\'{a}ndor and Kleist, Linda and Lamme, Jeroen S.K. and Oh, Eunjin and Wang, Yanheng},
  title =	{{Touring a Sequence of Orthogonal Polygons}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{50:1--50:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.50},
  URN =		{urn:nbn:de:0030-drops-264391},
  doi =		{10.4230/LIPIcs.ICALP.2026.50},
  annote =	{Keywords: shortest path, subquadratic time, dynamic planar distance oracle}
}
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)

Copy BibTex To Clipboard

@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.2026.23
Shortest Paths in Geodesic Unit-Disk Graphs

Authors: Bruce W. Brewer and Haitao Wang

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

Abstract
Let S be a set of n points in a polygon P with m vertices. The geodesic unit-disk graph G(S) induced by S has vertex set S and contains an edge between two vertices whenever their geodesic distance in P is at most one. In the weighted version, each edge is assigned weight equal to the geodesic distance between its endpoints; in the unweighted version, every edge has weight 1. Given a source point s ∈ S, we study the problem of computing shortest paths from s to all vertices of G(S). To the best of our knowledge, this problem has not been investigated previously. A naive approach constructs G(S) explicitly and then applies a standard shortest path algorithm for general graphs, but this requires quadratic time in the worst case, since G(S) may contain Ω(n²) edges. In this paper, we give the first subquadratic-time algorithms for this problem. For the weighted case, when P is a simple polygon, we obtain an O(m + n log³ n log² m)-time algorithm. For the unweighted case, we provide an O(m + n log n log² m)-time algorithm for simple polygons, and an O(√n (n+m)log(n+m))-time algorithm for polygons with holes.
Cite as

Bruce W. Brewer and Haitao Wang. Shortest Paths in Geodesic Unit-Disk Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{brewer_et_al:LIPIcs.SoCG.2026.23,
  author =	{Brewer, Bruce W. and Wang, Haitao},
  title =	{{Shortest Paths in Geodesic Unit-Disk Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{23:1--23:15},
  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.2026.23},
  URN =		{urn:nbn:de:0030-drops-258297},
  doi =		{10.4230/LIPIcs.SoCG.2026.23},
  annote =	{Keywords: unit-disk graph, geodesic distance, shortest paths, geodesic Voronoi diagrams, range emptiness queries, dynamic data structures}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.69
Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain

Authors: Joost van der Laan, Frank Staals, and Lorenzo Theunissen

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

Abstract
We present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain P with n vertices. Our goal is to store a dynamic set of m point sites S in P so that we can efficiently find a site s ∈ S closest to an arbitrary query point q. We will allow both insertions and deletions in the set of sites S. However, as even just computing the distance between an arbitrary pair of points q,s ∈ P requires a substantial amount of space, we allow for approximating the distances. Given a parameter ε > 0, we build an O(n/(ε)log n) space data structure that can compute a 1+ε-approximation of the distance between q and s in O((1/ε²)log n) time. Building on this, we then obtain an O((n+m)/ε log n + m/ε log m) space data structure that allows us to report a site s ∈ S so that the distance between query point q and s is at most (1+ε)-times the distance between q and its true nearest neighbor in O((1/ε²)log n + 1/(ε)log n log m + (1/ε)log² m) time. Our data structure supports updates in O((1/ε²)log n + (1/ε)log n log m + (1/ε)log² m) amortized time.
Cite as

Joost van der Laan, Frank Staals, and Lorenzo Theunissen. Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 69:1-69:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{vanderlaan_et_al:LIPIcs.SoCG.2026.69,
  author =	{van der Laan, Joost and Staals, Frank and Theunissen, Lorenzo},
  title =	{{Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{69:1--69:16},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-258769},
  doi =		{10.4230/LIPIcs.SoCG.2026.69},
  annote =	{Keywords: dynamic data structure, nearest neighbor search, polygonal domain}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.89
Approximating Convex Hulls via Range Queries

Authors: Thomas Schibler, Jie Xue, and Jiumu Zhu

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

Abstract
Recently, motivated by the rapid increase of the data size in various applications, Monemizadeh [APPROX'23] and Driemel, Monemizadeh, Oh, Staals, and Woodruff [SoCG'25] studied geometric problems in the setting where the only access to the input point set is via querying a range-search oracle. Algorithms in this setting are evaluated on two criteria: (i) the number of queries to the oracle and (ii) the error of the output. In this paper, we continue this line of research and investigate one of the most fundamental geometric problems in the oracle setting, i.e., the convex hull problem. Let P be an unknown set of points in [0,1]^d equipped with a range-emptiness oracle. Via querying the oracle, the algorithm is supposed to output a convex polygon C ⊆ [0,1]^d as an estimation of the convex hull CH(P) of P. The error of the output is defined as the volume of the symmetric difference C ⊕ CH(P) = (C∖CH(P)) ∪ (CH(P)∖C). We prove tight and near-tight tradeoffs between the number of queries and the error of the output for different variants of the problem, depending on the type of the range-emptiness queries and whether the queries are non-adaptive or adaptive. - Orthogonal emptiness queries in d-dimensional space: We show that the minimum error a deterministic algorithm can achieve with q queries is Θ(q^{-1/d}) if the queries are non-adaptive, and Θ(q^{-1/(d-1)}) if the queries are adaptive. In particular, in 2D, the bounds are Θ(1/√q) and Θ(1/q) for non-adaptive and adaptive queries, respectively. - Halfplane emptiness queries in 2D: We show that the minimum error a deterministic algorithm can achieve with q queries is Θ(1/√q) if the queries are non-adaptive, and Θ̃(1/q²) if the queries are adaptive. Here Θ̃(⋅) hides logarithmic factors.
Cite as

Thomas Schibler, Jie Xue, and Jiumu Zhu. Approximating Convex Hulls via Range Queries. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 89:1-89:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{schibler_et_al:LIPIcs.SoCG.2026.89,
  author =	{Schibler, Thomas and Xue, Jie and Zhu, Jiumu},
  title =	{{Approximating Convex Hulls via Range Queries}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{89:1--89:15},
  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.2026.89},
  URN =		{urn:nbn:de:0030-drops-258956},
  doi =		{10.4230/LIPIcs.SoCG.2026.89},
  annote =	{Keywords: convex hull, range searching}
}
Document
DOI: 10.4230/DagRep.15.5.64
Computational Geometry (Dagstuhl Seminar 25201)

Authors: Maarten Löffler, Eunjin Oh, Jeff M. Phillips, and Alexandra Weinberger

Published in: Dagstuhl Reports, Volume 15, Issue 5 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 25201 "Computational Geometry". The seminar program spanned the days from 11th May to 16th May 2025, and 39 participants from various countries were on site. Recent advances in computational geometry were presented and discussed, and new challenges were identified, in particular in relation to the two themes "parameterized complexity" and "the interplay between theory and implementation". This report collects the abstracts of the talks and the open problems presented at the seminar, an excerpt from the panel discussion, and partial progress from the active working groups.
Cite as

Maarten Löffler, Eunjin Oh, Jeff M. Phillips, and Alexandra Weinberger. Computational Geometry (Dagstuhl Seminar 25201). In Dagstuhl Reports, Volume 15, Issue 5, pp. 64-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@Article{loffler_et_al:DagRep.15.5.64,
  author =	{L\"{o}ffler, Maarten and Oh, Eunjin and Phillips, Jeff M. and Weinberger, Alexandra},
  title =	{{Computational Geometry (Dagstuhl Seminar 25201)}},
  pages =	{64--95},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{5},
  editor =	{L\"{o}ffler, Maarten and Oh, Eunjin and Phillips, Jeff M. and Weinberger, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.5.64},
  URN =		{urn:nbn:de:0030-drops-252780},
  doi =		{10.4230/DagRep.15.5.64},
  annote =	{Keywords: algorithms, combinatorics, complexity, geometric computing, implementation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.3
Parameterized Maximum Node-Disjoint Paths

Authors: Michael Lampis and Manolis Vasilakis

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We revisit the Maximum Node-Disjoint Paths problem, the natural optimization version of the famous Node-Disjoint Paths problem, where we are given an undirected graph G, k (demand) pairs of vertices (s_i, t_i), and an integer 𝓁, and are asked whether there exist at least 𝓁 vertex-disjoint paths in G whose endpoints are given pairs. This problem has been intensely studied from both the approximation and parameterized complexity point of view and is notably known to be intractable by standard structural parameters, such as tree-depth, as well as the combined parameter 𝓁 plus pathwidth. We present several results improving and clarifying this state of the art, with an emphasis towards FPT approximation. Our main positive contribution is to show that the problem’s intractability can be overcome using approximation: We show that for several of the structural parameters for which the problem is hard, most notably tree-depth, the problem admits an efficient FPT approximation scheme, returning a (1-ε)-approximate solution in time f(td,ε)n^𝒪(1). We manage to obtain these results by comprehensively mapping out the structural parameters for which the problem is FPT if 𝓁 is also a parameter, hence showing that understanding 𝓁 as a parameter is key to the problem’s approximability. This, in turn, is a problem we are able to solve via a surprisingly simple color-coding algorithm, which relies on identifying an insightful problem-specific variant of the natural parameter, namely the number of vertices used in the solution. The results above are quite encouraging, as they indicate that in some situations where the problem does not admit an FPT algorithm, it is still solvable almost to optimality in FPT time. A natural question is whether the FPT approximation algorithm we devised for tree-depth can be extended to pathwidth. We resolve this negatively, showing that under the Parameterized Inapproximability Hypothesis no FPT approximation scheme for this parameter is possible, even in time f(pw,ε)n^g(ε). We thus precisely determine the parameter border where the problem transitions from "hard but approximable" to "inapproximable". Lastly, we strengthen existing lower bounds by replacing W[1]-hardness by XNLP-completeness for parameter pathwidth, and improving the n^o(√{td}) ETH-based lower bound for tree-depth to (the optimal) n^o(td).
Cite as

Michael Lampis and Manolis Vasilakis. Parameterized Maximum Node-Disjoint Paths. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lampis_et_al:LIPIcs.IPEC.2025.3,
  author =	{Lampis, Michael and Vasilakis, Manolis},
  title =	{{Parameterized Maximum Node-Disjoint Paths}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.3},
  URN =		{urn:nbn:de:0030-drops-251357},
  doi =		{10.4230/LIPIcs.IPEC.2025.3},
  annote =	{Keywords: ETH, Maximum Node-Disjoint Paths, Parameterized Complexity, PIH}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.46
Realizing Metric Spaces with Convex Obstacles

Authors: Sándor Kisfaludi-Bak and Leonidas Theocharous

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The presence of obstacles has a significant impact on distance computation, motion-planning, and visibility. These problems have been studied extensively in the planar setting, while our understanding of these problems in 3- and higher-dimensional spaces is still rudimentary. In this paper, we study the impact of different types of obstacles on the induced geodesic metric in 3-dimensional Euclidean space. We say that a finite metric space (X, dist_X) is approximately realizable by a collection 𝒯 of obstacles in ℝ³ if for any ε > 0 it can be embedded into (ℝ³⧵⋃_{T∈𝒯} T, dist_𝒯) with worst-case multiplicative distortion 1+ε, where dist_𝒯 denotes the geodesic distance in the free space induced by 𝒯. We focus on three key geometric properties of obstacles -convexity, disjointness, and fatness- and examine how dropping each one of them affects the existence of such embeddings. Our main result concerns dropping the fatness property: we demonstrate that any finite metric space is realizable with 1+ε worst-case multiplicative distortion using a collection of convex and pairwise disjoint obstacles in ℝ³, even if the obstacles are congruent and equilateral triangles. Based on the same construction, we can also show that if we require fatness but drop any of the other two properties instead, then we can still approximately realize any finite metric space. Our results have important implications on the approximability of tsp with obstacles, a natural variant of tsp introduced recently by Alkema et al. (ESA 2022). Specifically, we use the recent results of Banerjee et al. on tsp in doubling spaces (FOCS 2024) and of Chew et al. on distances among obstacles (Inf. Process. Lett. 2002) to show that tsp with obstacles admits a PTAS if the obstacles are convex, fat, and pairwise disjoint. If any of these three properties is dropped, then our results, combined with the APX-hardness of Metric tsp, demonstrate that tsp with obstacles is APX-hard.
Cite as

Sándor Kisfaludi-Bak and Leonidas Theocharous. Realizing Metric Spaces with Convex Obstacles. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 46:1-46:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kisfaludibak_et_al:LIPIcs.ISAAC.2025.46,
  author =	{Kisfaludi-Bak, S\'{a}ndor and Theocharous, Leonidas},
  title =	{{Realizing Metric Spaces with Convex Obstacles}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{46:1--46:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.46},
  URN =		{urn:nbn:de:0030-drops-249545},
  doi =		{10.4230/LIPIcs.ISAAC.2025.46},
  annote =	{Keywords: traveling salesman, geodesic distance}
}
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)

Copy BibTex To Clipboard

@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
Complete Volume
DOI: 10.4230/LIPIcs.WADS.2025
LIPIcs, Volume 349, WADS 2025, Complete Volume

Authors: Pat Morin and Eunjin Oh

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

Abstract
LIPIcs, Volume 349, WADS 2025, Complete Volume
Cite as

19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 1-882, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@Proceedings{morin_et_al:LIPIcs.WADS.2025,
  title =	{{LIPIcs, Volume 349, WADS 2025, Complete Volume}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{1--882},
  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},
  URN =		{urn:nbn:de:0030-drops-245905},
  doi =		{10.4230/LIPIcs.WADS.2025},
  annote =	{Keywords: LIPIcs, Volume 349, WADS 2025, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.WADS.2025.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Pat Morin and Eunjin Oh

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{morin_et_al:LIPIcs.WADS.2025.0,
  author =	{Morin, Pat and Oh, Eunjin},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{0:i--0:xviii},
  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.2025.0},
  URN =		{urn:nbn:de:0030-drops-245890},
  doi =		{10.4230/LIPIcs.WADS.2025.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.42
The Parameterized Landscape of Labeled Graph Contractions

Authors: Manuel Lafond and Bertrand Marchand

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

Abstract
In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a parameterized complexity point of view, using parameters such as the maximum degree, the degeneracy, the clique-width or treewidth of the input graphs as well as the number of allowed contractions. We put this complexity in perspective with that of the labeled contractibility problem, i.e determining whether a labeled graph is a contraction of another. Surprisingly, our results indicate very little difference between these problems in terms of parameterized complexity status. We only prove their status to differ when parameterizing by both the degeneracy and the number of allowed contractions, showing W[1]-hardness of the maximum common contraction problem in this case, whereas the contractibility problem is FPT.
Cite as

Manuel Lafond and Bertrand Marchand. The Parameterized Landscape of Labeled Graph Contractions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lafond_et_al:LIPIcs.WADS.2025.42,
  author =	{Lafond, Manuel and Marchand, Bertrand},
  title =	{{The Parameterized Landscape of Labeled Graph Contractions}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{42:1--42:23},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-242732},
  doi =		{10.4230/LIPIcs.WADS.2025.42},
  annote =	{Keywords: Parameterized complexity - contractions - labels - widths}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.46
Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations

Authors: Vincent Pilaud and Aaron Williams

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

Abstract
Wiggly permutations were introduced by Bapat and Pilaud (Wigglyhedron Mathematische Zeitschrift 2025). We positively answer one of their conjectures by finding a Hamilton path in the wiggly flip graph that is isomorphic to the wigglyhedron. Our path provides a Gray code in which successive wiggly permutations are obtained by a single jump or hop, meaning that one or two consecutive symbols move past some number of smaller symbols. The Gray code has a simple greedy description that produces a recursive zig-zag pattern reminiscent of plain changes for permutations. More broadly, our results extend Algorithm J and the series of papers on zig-zag languages initiated by Hartung, Hoang, Mütze and Williams (Combinatorial Generation via Permutation Languages SODA 2020). Finally, we use wiggly changes as the basis for an 𝒪(n)-time delay generation algorithm.
Cite as

Vincent Pilaud and Aaron Williams. Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{pilaud_et_al:LIPIcs.WADS.2025.46,
  author =	{Pilaud, Vincent and Williams, Aaron},
  title =	{{Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{46:1--46:20},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-242778},
  doi =		{10.4230/LIPIcs.WADS.2025.46},
  annote =	{Keywords: permutations, wiggly permutations, pattern avoidance, permutahedron, wigglyhedron, Hamilton path, flip graph, Gray code, combinatorial generation, generation algorithm}
}
  • Refine by Type
  • 92 Document/PDF
  • 62 Document/HTML
  • 1 Volume

  • Refine by Publication Year
  • 6 2026
  • 63 2025
  • 5 2024
  • 1 2023
  • 2 2021
  • Show More...

  • Refine by Author
  • 32 Oh, Eunjin
  • 13 Ahn, Hee-Kap
  • 5 An, Shinwoo
  • 5 Bose, Prosenjit
  • 5 Wang, Haitao
  • Show More...

  • Refine by Series/Journal
  • 91 LIPIcs
  • 1 DagRep

  • Refine by Classification
  • 39 Theory of computation → Computational geometry
  • 14 Theory of computation → Design and analysis of algorithms
  • 8 Theory of computation → Parameterized complexity and exact algorithms
  • 4 Mathematics of computing → Graph algorithms
  • 4 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 4 geodesic distance
  • 4 simple polygons
  • 3 Geodesic distance
  • 3 facility location
  • 3 simple polygon
  • 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