24 Search Results for "Lochet, William"

Document
DOI: 10.4230/LIPIcs.STACS.2026.78
Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors

Authors: Roohani Sharma and Michał Włodarczyk

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Let ℱ be a finite family of graphs. In the ℱ-Deletion problem, one is given a graph G and an integer k, and the goal is to find k vertices whose deletion results in a graph with no minor from the family ℱ. This may be regarded as a far-reaching generalization of Vertex Cover and Feedback vertex Set. In their seminal work, Fomin, Lokshtanov, Misra & Saurabh [FOCS 2012] gave a polynomial kernel for this problem when the family ℱ contains a planar graph. As the size of their kernel is g(ℱ) ⋅ k^{f(ℱ)}, a natural follow-up question was whether the dependence on ℱ in the exponent of k can be avoided. The answer turned out to be negative: Giannopoulou, Jansen, Lokshtanov & Saurabh [TALG 2017] proved that this is already inevitable for the special case of the Treewidth-η-Deletion problem. In this work, we show that this non-uniformity can be avoided at the expense of a small loss. First, we present a simple 2-approximate kernelization algorithm for Treewidth-η-Deletion with a kernel size g(η) ⋅ k⁶. Next, we show that the approximation factor can be made arbitrarily close to 1, if we settle for a kernelization protocol with 𝒪(1) calls to an oracle that solves instances of size bounded by a uniform polynomial in k. We extend the above results to general ℱ-Deletion, whenever ℱ contains a planar graph, as long as an oracle for Treewidth-η-Deletion is available for small instances. Notably, all our constants are computable functions of ℱ and our techniques work also when some graphs in ℱ may be disconnected. Our results rely on two novel techniques. First, we transform so-called "near-protrusion decompositions" into true protrusion decompositions by sacrificing a small accuracy loss. Secondly, we show how to optimally compress such a decomposition with respect to general ℱ-Deletion. Using our second technique, we also obtain linear kernels on sparse graph classes when ℱ contains a planar graph, whereas the previously known theorems required all graphs in ℱ to be connected. Specifically, we generalize the kernelization algorithm by Kim, Langer, Paul, Reidl, Rossmanith, Sau & Sikdar [TALG 2015] on graph classes that exclude a topological minor.
Cite as

Roohani Sharma and Michał Włodarczyk. Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 78:1-78:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{sharma_et_al:LIPIcs.STACS.2026.78,
  author =	{Sharma, Roohani and W{\l}odarczyk, Micha{\l}},
  title =	{{Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{78:1--78:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.78},
  URN =		{urn:nbn:de:0030-drops-255674},
  doi =		{10.4230/LIPIcs.STACS.2026.78},
  annote =	{Keywords: kernelization, graph minors, treewidth, uniform kernels, minor hitting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.39
Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions

Authors: Keerti Choudhary, Amit Kumar, and Lakshay Saggi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs (s₁,t₁) and (s₂,t₂), decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent advances in disjoint shortest paths for DAGs and undirected graphs (Akmal et al. 2024), we present an O(mn log n)-time algorithm for this problem in weighted directed graphs that do not contain negative or zero weight cycles. This algorithm presents a significant improvement over the previously known O(m⁵n)-time bound (Berczi et al. 2017). Our approach exploits the algebraic structure of polynomials that enumerate shortest paths between terminal pairs. A key insight is that these polynomials admit a recursive decomposition, enabling efficient evaluation via dynamic programming over fields of characteristic two. Furthermore, we demonstrate how to report the corresponding paths in O(mn² log n)-time. In addition, we extend our techniques to a more general setting: given two terminal pairs (s₁, t₁) and (s₂, t₂) in a directed graph, find the minimum possible number of vertex intersections between any shortest path from s₁ to t₁ and s₂ to t₂. We call this the Minimum 2-Disjoint Shortest Paths (Min-2-DSP) problem. We provide in this paper the first efficient algorithm for this problem, including an O(m² n³)-time algorithm for directed graphs with positive edge weights, and an O(m+n)-time algorithm for DAGs and undirected graphs. Moreover, if the number of intersecting vertices is at least one, we show that it is possible to report the paths in the same O(m+n)-time. This is somewhat surprising, as there is no known o(mn) time algorithm for explicitly reporting the paths if they are vertex-disjoint, and is left as an open problem in (Akmal et al. 2024).
Cite as

Keerti Choudhary, Amit Kumar, and Lakshay Saggi. Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{choudhary_et_al:LIPIcs.ITCS.2026.39,
  author =	{Choudhary, Keerti and Kumar, Amit and Saggi, Lakshay},
  title =	{{Efficient Algorithms for the Disjoint Shortest Paths Problem and Its Extensions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{39:1--39:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.39},
  URN =		{urn:nbn:de:0030-drops-253267},
  doi =		{10.4230/LIPIcs.ITCS.2026.39},
  annote =	{Keywords: Disjoint paths, Disjoint shortest paths, Algebraic graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.10
Parameterized Complexity of Vehicle Routing

Authors: Michelle Döring, Jan Fehse, Tobias Friedrich, Paula Marten, Niklas Mohrin, Kirill Simonov, Farehe Soheil, Jakob Timm, and Shaily Verma

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

Abstract
The Vehicle Routing Problem (VRP) is a popular generalization of the Traveling Salesperson Problem. Instead of one salesperson traversing the entire weighted, undirected graph G, there are k vehicles available to jointly cover the set of clients C ⊆ V(G). Every vehicle must start at one of the depot vertices D ⊆ V(G) and return to its start. Capacitated Vehicle Routing (CVRP) additionally restricts the route of each vehicle by limiting the number of clients it can cover, the distance it can travel, or both. In this work, we study the complexity of VRP and the three variants of CVRP for several parameterizations, in particular focusing on the treewidth of G. We present an FPT algorithm for VRP parameterized by treewidth. For CVRP, we prove paraNP- and W[⋅]-hardness for various parameterizations, including treewidth, thereby rendering the existence of FPT algorithms unlikely. In turn, we provide an XP algorithm for CVRP when parameterized by both treewidth and the vehicle capacity.
Cite as

Michelle Döring, Jan Fehse, Tobias Friedrich, Paula Marten, Niklas Mohrin, Kirill Simonov, Farehe Soheil, Jakob Timm, and Shaily Verma. Parameterized Complexity of Vehicle Routing. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doring_et_al:LIPIcs.IPEC.2025.10,
  author =	{D\"{o}ring, Michelle and Fehse, Jan and Friedrich, Tobias and Marten, Paula and Mohrin, Niklas and Simonov, Kirill and Soheil, Farehe and Timm, Jakob and Verma, Shaily},
  title =	{{Parameterized Complexity of Vehicle Routing}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{10:1--10:17},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-251424},
  doi =		{10.4230/LIPIcs.IPEC.2025.10},
  annote =	{Keywords: Vehicle Routing Problem, Treewidth, Parameterized Complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

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

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.46
Max-Distance Sparsification for Diversification and Clustering

Authors: Soh Kumabe

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

Abstract
Let 𝒟 be a set family that is the solution domain of some combinatorial problem. The max-min diversification problem on 𝒟 is the problem to select k sets from 𝒟 such that the Hamming distance between any two selected sets is at least d. FPT algorithms parameterized by k+𝓁, where 𝓁 = max_{D ∈ 𝒟}|D|, and k+d have been actively studied recently for several specific domains. This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization k+𝓁 and k+d, we provide an FPT oracle algorithm for the max-min diversification problem using oracles related to 𝒟. We then demonstrate that our frameworks provide the first FPT algorithms on several new domains 𝒟, including the domain of t-linear matroid intersection, almost 2-SAT, minimum edge s,t-flows, vertex sets of s,t-mincut, vertex sets of edge bipartization, and Steiner trees. We also demonstrate that our frameworks generalize most of the existing domain-specific tractability results. Our main technical breakthrough is introducing the notion of max-distance sparsifier of 𝒟, a domain on which the max-min diversification problem is equivalent to the same problem on the original domain 𝒟. The core of our framework is to design FPT oracle algorithms that construct a constant-size max-distance sparsifier of 𝒟. Using max-distance sparsifiers, we provide FPT algorithms for the max-min and max-sum diversification problems on 𝒟, as well as k-center and k-sum-of-radii clustering problems on 𝒟, which are also natural problems in the context of diversification and have their own interests.
Cite as

Soh Kumabe. Max-Distance Sparsification for Diversification and Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ESA.2025.46,
  author =	{Kumabe, Soh},
  title =	{{Max-Distance Sparsification for Diversification and Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{46:1--46:14},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-245146},
  doi =		{10.4230/LIPIcs.ESA.2025.46},
  annote =	{Keywords: Fixed-Parameter Tractability, Diversification, Clustering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.62
Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering

Authors: Sina Bagheri Nezhad, Sayan Bandyapadhyay, and Tianzhi Chen

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

Abstract
In a seminal work, Chierichetti et al. [Chierichetti et al., 2017] introduced the (t,k)-fair clustering problem: Given a set of red points and a set of blue points in a metric space, a clustering is called fair if the number of red points in each cluster is at most t times and at least 1/t times the number of blue points in that cluster. The goal is to compute a fair clustering with at most k clusters that optimizes certain objective function. Considering this problem, they designed a polynomial-time O(1)- and O(t)-approximation for the k-center and the k-median objective, respectively. Recently, Carta et al. [Carta et al., 2024] studied this problem with the sum-of-radii objective and obtained a (6+ε)-approximation with running time O((k log_{1+ε}(k/ε))^k n^O(1)), i.e., fixed-parameter tractable in k. Here n is the input size. In this work, we design the first polynomial-time O(1)-approximation for (t,k)-fair clustering with the sum-of-radii objective, improving the result of Carta et al. Our result places sum-of-radii in the same group of objectives as k-center, that admit polynomial-time O(1)-approximations. This result also implies a polynomial-time O(1)-approximation for the Euclidean version of the problem, for which an f(k)⋅n^O(1)-time (1+ε)-approximation was known due to Drexler et al. [Drexler et al., 2023]. Here f is an exponential function of k. We are also able to extend our result to any arbitrary 𝓁 ≥ 2 number of colors when t = 1. This matches known results for the k-center and k-median objectives in this case. The significant disparity of sum-of-radii compared to k-center and k-median presents several complex challenges, all of which we successfully overcome in our work. Our main contribution is a novel cluster-merging-based analysis technique for sum-of-radii that helps us achieve the constant-approximation bounds.
Cite as

Sina Bagheri Nezhad, Sayan Bandyapadhyay, and Tianzhi Chen. Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 62:1-62:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bagherinezhad_et_al:LIPIcs.ESA.2025.62,
  author =	{Bagheri Nezhad, Sina and Bandyapadhyay, Sayan and Chen, Tianzhi},
  title =	{{Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{62:1--62:16},
  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.2025.62},
  URN =		{urn:nbn:de:0030-drops-245309},
  doi =		{10.4230/LIPIcs.ESA.2025.62},
  annote =	{Keywords: fair clustering, sum-of-radii clustering, approximation algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.23
Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints

Authors: Sayan Bandyapadhyay and Tianzhi Chen

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In this work, we study k-min-sum-of-radii (k-MSR) clustering under mergeable constraints. k-MSR seeks to group data points using a set of up to k balls, such that the sum of the radii of the balls is minimized. A clustering constraint is called mergeable if merging two clusters satisfying the constraint, results in a cluster that also satisfies the constraint. Many popularly studied constraints are mergeable, including fairness constraints and lower bound constraints. In our work, we design a (4+ε)-approximation for k-MSR under any given mergeable constraint with runtime 2^{O(k/(ε)⋅log²k/ε)} n⁴, i.e., fixed-parameter tractable in k for constant ε. Our result directly improves upon the FPT (6+ε)-approximation by Carta et al. [Carta et al., 2024]. We also provide a hardness result that excludes the exact solvability of k-MSR under any given mergeable constraint in time f(k)n^o(k), assuming ETH is true.
Cite as

Sayan Bandyapadhyay and Tianzhi Chen. Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.APPROX/RANDOM.2025.23,
  author =	{Bandyapadhyay, Sayan and Chen, Tianzhi},
  title =	{{Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.23},
  URN =		{urn:nbn:de:0030-drops-243894},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.23},
  annote =	{Keywords: sum-of-radii clustering, mergeable constraints, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.38
Clustering Point Sets Revisited

Authors: Md. Billal Hossain and Benjamin Raichel

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

Abstract
In the sets clustering problem one is given a collection of point sets 𝒫 = {P_1,… P_m} in ℝ^d, where for any set of k centers in ℝ^d, each P_i is assigned to its nearest center as determine by some local cost functions. The goal is then to select a set of k centers to minimize some global cost function of the corresponding local assignment costs. Specifically, we consider either summing or taking the maximum cost over all P_i, where for each P_i the cost of assigning it to a center c is either max_{p ∈ P_i} ‖c-p‖, ∑_{p ∈ P_i} ‖c-p‖, or ∑_{p ∈ P_i} ‖c-p‖². Different combinations of the global and local cost functions naturally generalize the k-center, k-median, and k-means clustering problems. In this paper, we improve the prior results for the natural generalization of k-center, give the first result for the natural generalization of k-means, and give results for generalizations of k-median and k-center which differ from those previously studied.
Cite as

Md. Billal Hossain and Benjamin Raichel. Clustering Point Sets Revisited. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hossain_et_al:LIPIcs.WADS.2025.38,
  author =	{Hossain, Md. Billal and Raichel, Benjamin},
  title =	{{Clustering Point Sets Revisited}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{38:1--38:16},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-242693},
  doi =		{10.4230/LIPIcs.WADS.2025.38},
  annote =	{Keywords: Clustering, k-center, k-median, k-means}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.17
Robust Contraction Decomposition for Minor-Free Graphs and Its Applications

Authors: Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov, Dániel Marx, Pranabendu Misra, Daniel Neuen, Saket Saurabh, Prafullkumar Tale, and Jie Xue

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

Abstract
We prove a robust contraction decomposition theorem for H-minor-free graphs, which states that given an H-minor-free graph G and an integer p, one can partition in polynomial time the vertices of G into p sets Z₁,… ,Z_p such that tw(G/(Z_i ⧵ Z')) = O(p + |Z'|) for all i ∈ [p] and Z' ⊆ Z_i. Here, tw(⋅) denotes the treewidth of a graph and G/(Z_i ⧵ Z') denotes the graph obtained from G by contracting all edges with both endpoints in Z_i ⧵ Z'. Our result generalizes earlier results by Klein [SICOMP 2008] and Demaine et al. [STOC 2011] based on partitioning E(G), and some recent theorems for planar graphs by Marx et al. [SODA 2022], for bounded-genus graphs (more generally, almost-embeddable graphs) by Bandyapadhyay et al. [SODA 2022], and for unit-disk graphs by Bandyapadhyay et al. [SoCG 2022]. The robust contraction decomposition theorem directly results in parameterized algorithms with running time 2^{Õ(√k)} ⋅ n^{O(1)} or n^{O(√k)} for every vertex/edge deletion problems on H-minor-free graphs that can be formulated as Permutation CSP Deletion or 2-Conn Permutation CSP Deletion. Consequently, we obtain the first subexponential-time parameterized algorithms for Subset Feedback Vertex Set, Subset Odd Cycle Transversal, Subset Group Feedback Vertex Set, 2-Conn Component Order Connectivity on H-minor-free graphs. For other problems which already have subexponential-time parameterized algorithms on H-minor-free graphs (e.g., Odd Cycle Transversal, Vertex Multiway Cut, Vertex Multicut, etc.), our theorem gives much simpler algorithms of the same running time.
Cite as

Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov, Dániel Marx, Pranabendu Misra, Daniel Neuen, Saket Saurabh, Prafullkumar Tale, and Jie Xue. Robust Contraction Decomposition for Minor-Free Graphs and Its Applications. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.ICALP.2025.17,
  author =	{Bandyapadhyay, Sayan and Lochet, William and Lokshtanov, Daniel and Marx, D\'{a}niel and Misra, Pranabendu and Neuen, Daniel and Saurabh, Saket and Tale, Prafullkumar and Xue, Jie},
  title =	{{Robust Contraction Decomposition for Minor-Free Graphs and Its Applications}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{17:1--17:19},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-233948},
  doi =		{10.4230/LIPIcs.ICALP.2025.17},
  annote =	{Keywords: subexponential time algorithms, graph decomposition, planar graphs, minor-free graphs, graph contraction}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.53
A PTAS for TSP with Neighbourhoods over Parallel Line Segments

Authors: Benyamin Ghaseminia and Mohammad R. Salavatipour

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

Abstract
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane (ℝ²) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between [1, λ] for any constant value λ ≥ 1. In TSPN (which generalizes classic TSP), each client represents a set (or neighbourhood) of points in a metric and the goal is to find a minimum cost TSP tour that visits at least one point from each client set. In the Euclidean setting, each neighbourhood is a region on the plane. TSPN is significantly more difficult than classic TSP even in the Euclidean setting, as it captures group TSP. A notable case of TSPN is when each neighbourhood is a line segment. Although there are PTASs for when neighbourhoods are fat objects (with limited overlap), TSPN over line segments is APX-hard even if all the line segments have unit length. For parallel (unit) line segments, the best approximation factor is 3√2 from more than two decades ago. The PTAS we present in this paper settles the approximability of this case of the problem. Our algorithm finds a (1 + ε)-factor approximation for an instance of the problem for n segments with lengths in [1,λ] in time n^O(λ/ε³).
Cite as

Benyamin Ghaseminia and Mohammad R. Salavatipour. A PTAS for TSP with Neighbourhoods over Parallel Line Segments. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghaseminia_et_al:LIPIcs.SoCG.2025.53,
  author =	{Ghaseminia, Benyamin and Salavatipour, Mohammad R.},
  title =	{{A PTAS for TSP with Neighbourhoods over Parallel Line Segments}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{53:1--53:15},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-232058},
  doi =		{10.4230/LIPIcs.SoCG.2025.53},
  annote =	{Keywords: Approximation Scheme, TSP Neighbourhood, Parallel line segments}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.17
Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths

Authors: Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach

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

Abstract
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) n-vertex graph G along with k terminal pairs (s_1,t_1),(s_2,t_2),…,(s_k,t_k). The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of k. Lochet’s result implies the existence of a polynomial-time ck-approximation for Maximum Vertex-Disjoint Shortest Paths, where c ≤ 1 is a constant. (One can guess 1/c terminal pairs to connect in k^O(1/c) time and then utilize Lochet’s algorithm to compute the solution in n^f(1/c) time.) Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an o(k)-approximation within f(k) ⋅ poly(n) time for any function f that only depends on k. Our second result demonstrates the infeasibility of achieving an approximation ratio of m^{1/2-ε} in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a ⌈√𝓁⌉-approximation, where 𝓁 is the number of edges in all the paths of an optimal solution. Since 𝓁 ≤ n, this underscores the tightness of the m^{1/2-ε}-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by 𝓁 but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.
Cite as

Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach. Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2025.17,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A.},
  title =	{{Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{17:1--17:17},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-228422},
  doi =		{10.4230/LIPIcs.STACS.2025.17},
  annote =	{Keywords: Inapproximability, Fixed-parameter tractability, Parameterized approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.52
Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion

Authors: Séhane Bel Houari-Durand, Eduard Eiben, and Magnus Wahlström

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

Abstract
Given a graph G and an integer k, the H-free Edge Deletion problem asks whether there exists a set of at most k edges of G whose deletion makes G free of induced copies of H. Significant attention has been given to the kernelizability aspects of this problem - i.e., for which graphs H does the problem admit an "efficient preprocessing" procedure, known as a polynomial kernelization, where an instance I of the problem with parameter k is reduced to an equivalent instance I' whose size and parameter value are bounded polynomially in k? Although such routines are known for many graphs H where the class of H-free graphs has significant restricted structure, it is also clear that for most graphs H the problem is incompressible, i.e., admits no polynomial kernelization parameterized by k unless the polynomial hierarchy collapses. These results led Marx and Sandeep to the conjecture that H-free Edge Deletion is incompressible for any graph H with at least five vertices, unless H is complete or has at most one edge (JCSS 2022). This conjecture was reduced to the incompressibility of H-free Edge Deletion for a finite list of graphs H. We consider one of these graphs, which we dub the prison, and show that Prison-Free Edge Deletion has a polynomial kernel, refuting the conjecture. On the other hand, the same problem for the complement of the prison is incompressible.
Cite as

Séhane Bel Houari-Durand, Eduard Eiben, and Magnus Wahlström. Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{houaridurand_et_al:LIPIcs.STACS.2025.52,
  author =	{Houari-Durand, S\'{e}hane Bel and Eiben, Eduard and Wahlstr\"{o}m, Magnus},
  title =	{{Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{52:1--52:17},
  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.2025.52},
  URN =		{urn:nbn:de:0030-drops-228770},
  doi =		{10.4230/LIPIcs.STACS.2025.52},
  annote =	{Keywords: Graph modification problems, parameterized complexity, polynomial kernelization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.15
Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems

Authors: Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest known (exponential-time) exact algorithms and the best known approximation factors that can be achieved in polynomial time? Following the recent research initiated by Esmer et al. (ESA 2022, IPEC 2023, SODA 2024) on vertex-subset problems, and by Inamdar et al. (ITCS 2024) on graph-partitioning problems, we focus on vertex-ordering problems. In particular, we give positive results for Feedback Arc Set, Optimal Linear Arrangement, Cutwidth, and Pathwidth. Most of our algorithms build upon a novel "balanced-cut" approach - which is our main conceptual contribution. This allows us to solve various problems in very general settings allowing for directed and arc-weighted input graphs. Our main technical contribution is a (1+ε)-approximation for any ε > 0 for (weighted) Feedback Arc Set in O^*((2-δ_ε)^n) time, where δ_ε > 0 is a constant only depending on ε.
Cite as

Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh. Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.ITCS.2025.15,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Inamdar, Tanmay and Saurabh, Saket},
  title =	{{Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-226431},
  doi =		{10.4230/LIPIcs.ITCS.2025.15},
  annote =	{Keywords: Feedback Arc Set, Cutwidth, Optimal Linear Arrangement, Pathwidth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.46
Uniform Polynomial Kernel for Deletion to K_{2,p} Minor-Free Graphs

Authors: William Lochet and Roohani Sharma

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

Abstract
In the F-Deletion problem, where F is a fixed finite family of graphs, the input is a graph G and an integer k, and the goal is to determine if there exists a set of at most k vertices whose deletion results in a graph that does not contain any graph of F as a minor. The F-Deletion problem encapsulates a large class of natural and interesting graph problems like Vertex Cover, Feedback Vertex Set, Treewidth-η Deletion, Treedepth-η Deletion, Pathwidth-η Deletion, Outerplanar Deletion, Vertex Planarization and many more. We study the F-Deletion problem from the kernelization perspective. In a seminal work, Fomin et al. [FOCS 2012] gave a polynomial kernel for this problem when the family F contains at least one planar graph. The asymptotic growth of the size of the kernel is not uniform with respect to the family F: that is, the size of the kernel is k^{f(F)}, for some function f that depends only on F. Later Giannopoulou et al. [TALG 2017] showed that the non-uniformity in the kernel size bound is unavoidable as Treewidth-η Deletion cannot admit a kernel of size 𝒪(k^{(η+1)/2 - ε}), for any ε > 0, unless NP ⊆ coNP/poly. On the other hand it was also shown that Treedepth-η Deletion admits a uniform kernel of size f(F) ⋅ k⁶ depicting that there are subclasses of F where the asymptotic kernel sizes do not grow as a function of the family F. This work led to the question of determining classes of F where the problem admits uniform polynomial kernels. In this paper, we show that if all the graphs in F are connected and ℱ contains K_{2,p} (a bipartite graph with 2 vertices on one side and p vertices on the other), then the problem admits a uniform kernel of size f(F) ⋅ k^10. The graph K_{2,p} is one natural extension of the graph θ_p, where θ_p is a graph on two vertices and p parallel edges. The case when F contains θ_p has been studied earlier and serves as (the only) other example where the problem admits a uniform polynomial kernel.
Cite as

William Lochet and Roohani Sharma. Uniform Polynomial Kernel for Deletion to K_{2,p} Minor-Free Graphs. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lochet_et_al:LIPIcs.ISAAC.2024.46,
  author =	{Lochet, William and Sharma, Roohani},
  title =	{{Uniform Polynomial Kernel for Deletion to K\underline\{2,p\} Minor-Free Graphs}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{46:1--46:14},
  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.2024.46},
  URN =		{urn:nbn:de:0030-drops-221731},
  doi =		{10.4230/LIPIcs.ISAAC.2024.46},
  annote =	{Keywords: Uniform polynomial kernel, ℱ-minor-free deletion, complete bipartite minor-free graphs, K\underline\{2,p\}, protrusions}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.11
Minimum-Membership Geometric Set Cover, Revisited

Authors: Sayan Bandyapadhyay, William Lochet, Saket Saurabh, and Jie Xue

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We revisit a natural variant of the geometric set cover problem, called minimum-membership geometric set cover (MMGSC). In this problem, the input consists of a set S of points and a set ℛ of geometric objects, and the goal is to find a subset ℛ^* ⊆ ℛ to cover all points in S such that the membership of S with respect to ℛ^*, denoted by memb(S,ℛ^*), is minimized, where memb(S,ℛ^*) = max_{p ∈ S} |{R ∈ ℛ^*: p ∈ R}|. We give the first polynomial-time approximation algorithms for MMGSC in ℝ². Specifically, we achieve the following two main results. - We give the first polynomial-time constant-approximation algorithm for MMGSC with unit squares. This answers a question left open since the work of Erlebach and Leeuwen [SODA'08], who gave a constant-approximation algorithm with running time n^{O(opt)} where opt is the optimum of the problem (i.e., the minimum membership). - We give the first polynomial-time approximation scheme (PTAS) for MMGSC with halfplanes. Prior to this work, it was even unknown whether the problem can be approximated with a factor of o(log n) in polynomial time, while it is well-known that the minimum-size set cover problem with halfplanes can be solved in polynomial time. We also consider a problem closely related to MMGSC, called minimum-ply geometric set cover (MPGSC), in which the goal is to find ℛ^* ⊆ ℛ to cover S such that the ply of ℛ^* is minimized, where the ply is defined as the maximum number of objects in ℛ^* which have a nonempty common intersection. Very recently, Durocher et al. gave the first constant-approximation algorithm for MPGSC with unit squares which runs in O(n^{12}) time. We give a significantly simpler constant-approximation algorithm with near-linear running time.
Cite as

Sayan Bandyapadhyay, William Lochet, Saket Saurabh, and Jie Xue. Minimum-Membership Geometric Set Cover, Revisited. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.11,
  author =	{Bandyapadhyay, Sayan and Lochet, William and Saurabh, Saket and Xue, Jie},
  title =	{{Minimum-Membership Geometric Set Cover, Revisited}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.11},
  URN =		{urn:nbn:de:0030-drops-178610},
  doi =		{10.4230/LIPIcs.SoCG.2023.11},
  annote =	{Keywords: geometric set cover, geometric optimization, approximation algorithms}
}
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