7 Search Results for "Rösner, Clemens"

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
DOI: 10.4230/LIPIcs.ESA.2025.63
Connected k-Median with Disjoint and Non-Disjoint Clusters

Authors: Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt

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

Abstract
The connected k-median problem is a constrained clustering problem that combines distance-based k-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that is completely unrelated to the metric space. The goal is to compute k centers and corresponding clusters such that each cluster forms a connected subgraph of G, and such that the k-median cost is minimized. The problem has applications in very different fields like geodesy (particularly districting), social network analysis (especially community detection), or bioinformatics. We study a version with overlapping clusters where points can be part of multiple clusters which is natural for the use case of community detection. This problem variant is Ω(log n)-hard to approximate, and our main result is an 𝒪(k² log n)-approximation algorithm for the problem. We complement it with an Ω(n^{1-ε})-hardness result for the case of disjoint clusters without overlap with general connectivity graphs, as well as an exact algorithm in this setting if the connectivity graph is a tree.
Cite as

Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt. Connected k-Median with Disjoint and Non-Disjoint Clusters. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eube_et_al:LIPIcs.ESA.2025.63,
  author =	{Eube, Jan and Luo, Kelin and Reineccius, Dorian and R\"{o}glin, Heiko and Schmidt, Melanie},
  title =	{{Connected k-Median with Disjoint and Non-Disjoint Clusters}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{63:1--63:14},
  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.2025.63},
  URN =		{urn:nbn:de:0030-drops-245317},
  doi =		{10.4230/LIPIcs.ESA.2025.63},
  annote =	{Keywords: Clustering, Connectivity constraints, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.105
Parameterized Algorithms for Computing Pareto Sets

Authors: Joshua Marc Könen, Heiko Röglin, and Tarek Stuck

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

Abstract
The problem of computing the set of Pareto-optimal solutions has been studied for a variety of multiobjective optimization problems. For many such problems, algorithms are known that compute the Pareto set in (weak) output-polynomial time. These algorithms are often based on dynamic programming and by weak output-polynomial time, we mean that the running time depends polynomially on the size of the Pareto set but also on the sizes of the Pareto sets of the subproblems that occur in the dynamic program. For some problems, like the multiobjective minimum spanning tree problem, such algorithms are not known to exist and for other problems, like multiobjective versions of many NP-hard problems, such algorithms cannot exist, unless 𝒫 = 𝒩𝒫. Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first derive an algorithm to compute the Pareto set for the multicriteria s-t cut problem and show how this result can be applied to a polygon aggregation problem arising in cartography that has recently been introduced by Rottmann et al. (GIScience 2021). We also show how to apply these techniques to also compute the Pareto set of the multiobjective minimum spanning tree problem and for the multiobjective TSP. The running time of our algorithms is O(f(w)⋅poly(n,p_{max})), where f is some function in the treewidth w, n is the input size, and p_{max} is an upper bound on the size of the Pareto sets of the subproblems that occur in the dynamic program. Finally, we present an experimental evaluation of computing Pareto sets on real-world instances of polygon aggregation problems. For this matter we devised a task-specific data structure that allows for efficient storage and modification of large sets of Pareto-optimal solutions. Throughout the implementation process, we incorporated several improved strategies and heuristics that significantly reduced both runtime and memory usage, enabling us to solve instances with treewidth of up to 22 within reasonable amount of time. Moreover, we conducted a preprocessing study to compare different tree decompositions in terms of their estimated overall runtime.
Cite as

Joshua Marc Könen, Heiko Röglin, and Tarek Stuck. Parameterized Algorithms for Computing Pareto Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 105:1-105:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{konen_et_al:LIPIcs.ESA.2025.105,
  author =	{K\"{o}nen, Joshua Marc and R\"{o}glin, Heiko and Stuck, Tarek},
  title =	{{Parameterized Algorithms for Computing Pareto Sets}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{105:1--105:15},
  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.2025.105},
  URN =		{urn:nbn:de:0030-drops-245749},
  doi =		{10.4230/LIPIcs.ESA.2025.105},
  annote =	{Keywords: parameterized algorithms, treewidth, multicriteria optimization problems, multicriteria MST, multicriteria TSP, polygon aggregation}
}
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.ISAAC.2024.16
FPT Approximations for Fair k-Min-Sum-Radii

Authors: Lena Carta, Lukas Drexler, Annika Hennes, Clemens Rösner, and Melanie Schmidt

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

Abstract
We consider the k-min-sum-radii (k-MSR) clustering problem with fairness constraints. The k-min-sum-radii problem is a mixture of the classical k-center and k-median problems. We are given a set of points P in a metric space and a number k and aim to partition the points into k clusters, each of the clusters having one designated center. The objective to minimize is the sum of the radii of the k clusters (where in k-center we would only consider the maximum radius and in k-median we would consider the sum of the individual points' costs). Various notions of fair clustering have been introduced lately, and we follow the definitions due to Chierichetti et al. [Flavio Chierichetti et al., 2017] which demand that cluster compositions shall follow the proportions of the input point set with respect to some given sensitive attribute. For the easier case where the sensitive attribute only has two possible values and each is equally frequent in the input, the aim is to compute a clustering where all clusters have a 1:1 ratio with respect to this attribute. We call this the 1:1 case. There has been a surge of FPT-approximation algorithms for the k-MSR problem lately, solving the problem both in the unconstrained case and in several constrained problem variants. We add to this research area by designing an FPT (6+ε)-approximation that works for k-MSR under the mentioned general fairness notion. For the special 1:1 case, we improve our algorithm to achieve a (3+ε)-approximation.
Cite as

Lena Carta, Lukas Drexler, Annika Hennes, Clemens Rösner, and Melanie Schmidt. FPT Approximations for Fair k-Min-Sum-Radii. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{carta_et_al:LIPIcs.ISAAC.2024.16,
  author =	{Carta, Lena and Drexler, Lukas and Hennes, Annika and R\"{o}sner, Clemens and Schmidt, Melanie},
  title =	{{FPT Approximations for Fair k-Min-Sum-Radii}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{16:1--16:18},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-221438},
  doi =		{10.4230/LIPIcs.ISAAC.2024.16},
  annote =	{Keywords: Clustering, k-min-sum-radii, fairness}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.18
On the Cost of Essentially Fair Clusterings

Authors: Ioana O. Bercea, Martin Groß, Samir Khuller, Aounon Kumar, Clemens Rösner, Daniel R. Schmidt, and Melanie Schmidt

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
Clustering is a fundamental tool in data mining and machine learning. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters - especially if the data is already biased. At NIPS 2017, Chierichetti et al. [Flavio Chierichetti et al., 2017] proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair k-center problem and a O(t)-approximation for the fair k-median problem, where t is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair k-center [Clemens Rösner and Melanie Schmidt, 2018]. We extend and improve the known results. Firstly, we give a 5-approximation for the fair k-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives k-center, k-supplier, k-median, k-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed.
Cite as

Ioana O. Bercea, Martin Groß, Samir Khuller, Aounon Kumar, Clemens Rösner, Daniel R. Schmidt, and Melanie Schmidt. On the Cost of Essentially Fair Clusterings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bercea_et_al:LIPIcs.APPROX-RANDOM.2019.18,
  author =	{Bercea, Ioana O. and Gro{\ss}, Martin and Khuller, Samir and Kumar, Aounon and R\"{o}sner, Clemens and Schmidt, Daniel R. and Schmidt, Melanie},
  title =	{{On the Cost of Essentially Fair Clusterings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.18},
  URN =		{urn:nbn:de:0030-drops-112337},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.18},
  annote =	{Keywords: approximation, clustering, fairness, LP rounding}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.96
Privacy Preserving Clustering with Constraints

Authors: Clemens Rösner and Melanie Schmidt

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized. The problem allows for elegant 2-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem. We raise the question whether general methods can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that respects one constraint more. Our constraint of choice is privacy: Here, we are asked to only open a center when at least l clients will be assigned to it. We show how to combine privacy with several other constraints.
Cite as

Clemens Rösner and Melanie Schmidt. Privacy Preserving Clustering with Constraints. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 96:1-96:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{rosner_et_al:LIPIcs.ICALP.2018.96,
  author =	{R\"{o}sner, Clemens and Schmidt, Melanie},
  title =	{{Privacy Preserving Clustering with Constraints}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{96:1--96:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.96},
  URN =		{urn:nbn:de:0030-drops-91008},
  doi =		{10.4230/LIPIcs.ICALP.2018.96},
  annote =	{Keywords: Clustering, k-center, Constraints, Privacy, Lower Bounds, Fairness}
}
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