8 Search Results for "Negahbani, Maryam"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.19
Clustering in Varying Metrics

Authors: Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We introduce the aggregated clustering problem, where one is given T instances of a center-based clustering task over the same n points, but under different metrics. The goal is to open k centers to minimize an aggregate of the clustering costs - e.g., the average or maximum - where the cost is measured via k-center/median/means objectives. More generally, we minimize a norm Ψ over the T cost values. We show that for T ≥ 3, the problem is inapproximable to any finite factor in polynomial time. For T = 2, we give constant-factor approximations. We also show W[2]-hardness when parameterized by k, but obtain f(k,T)poly(n)-time 3-approximations when parameterized by both k and T. When the metrics have structure, we obtain efficient parameterized approximation schemes (EPAS). If all T metrics have bounded ε-scatter dimension, we achieve a (1+ε)-approximation in f(k,T,ε)poly(n) time. If the metrics are induced by edge weights on a common graph G of bounded treewidth tw, and Ψ is the sum function, we get an EPAS in f(T,ε,tw)poly(n,k) time. Conversely, unless (randomized) ETH is false, any finite factor approximation is impossible if parametrized by only T, even when the treewidth is tw = Ω(polylog n).
Cite as

Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar. Clustering in Varying Metrics. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chakrabarty_et_al:LIPIcs.FSTTCS.2025.19,
  author =	{Chakrabarty, Deeparnab and Conroy, Jonathan and Sarkar, Ankita},
  title =	{{Clustering in Varying Metrics}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251007},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.19},
  annote =	{Keywords: Clustering, approximation algorithms, LP rounding, parameterized and exact algorithms, dynamic programming, fixed parameter tractability, hardness of approximation}
}
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.FORC.2025.20
Group Fairness and Multi-Criteria Optimization in School Assignment

Authors: Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the problem of assigning students to schools when students have different utilities for schools and schools have limited capacities. The students belong to demographic groups, and fairness over these groups is captured either by concave objectives, or additional constraints on the utility of the groups. We present approximation algorithms for this assignment problem with group fairness via convex program rounding. These algorithms achieve various trade-offs between capacity violation and running time. We also show that our techniques easily extend to the setting where there are arbitrary constraints on the feasible assignment, capturing multi-criteria optimization. We present simulation results that demonstrate that the rounding methods are practical even on large problem instances, with the empirical capacity violation being much better than the theoretical bounds.
Cite as

Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar. Group Fairness and Multi-Criteria Optimization in School Assignment. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{k.a._et_al:LIPIcs.FORC.2025.20,
  author =	{K. A., Santhini and Munagala, Kamesh and Nasre, Meghana and S. Sankar, Govind},
  title =	{{Group Fairness and Multi-Criteria Optimization in School Assignment}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.20},
  URN =		{urn:nbn:de:0030-drops-231471},
  doi =		{10.4230/LIPIcs.FORC.2025.20},
  annote =	{Keywords: School Assignment, Approximation Algorithms, Group Fairness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.33
Approximation Algorithms for Continuous Clustering and Facility Location Problems

Authors: Deeparnab Chakrabarty, Maryam Negahbani, and Ankita Sarkar

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
In this paper, we consider center-based clustering problems where C, the set of points to be clustered, lies in a metric space (X,d), and the set X of candidate centers is potentially infinite-sized. We call such problems continuous clustering problems to differentiate them from the discrete clustering problems where the set of candidate centers is explicitly given. It is known that for many objectives, when one restricts the set of centers to C itself and applies an α_dis-approximation algorithm for the discrete version, one obtains a β ⋅ α_{dis}-approximation algorithm for the continuous version via the triangle inequality property of the distance function. Here β depends on the objective, and for many objectives such as k-median, β = 2, while for some others such as k-means, β = 4. The motivating question in this paper is whether this gap of factor β between continuous and discrete problems is inherent, or can one design better algorithms for continuous clustering than simply reducing to the discrete case as mentioned above? In a recent SODA 2021 paper, Cohen-Addad, Karthik, and Lee prove a factor-2 and a factor-4 hardness, respectively, for the continuous versions of the k-median and k-means problems, even when the number of cluster centers is a constant. The discrete problem for a constant number of centers is easily solvable exactly using enumeration, and therefore, in certain regimes, the "β-factor loss" seems unavoidable. In this paper, we describe a technique based on the round-or-cut framework to approach continuous clustering problems. We show that, for the continuous versions of some clustering problems, we can design approximation algorithms attaining a better factor than the β-factor blow-up mentioned above. In particular, we do so for: the uncapacitated facility location problem with uniform facility opening costs (λ-UFL); the k-means problem; the individually fair k-median problem; and the k-center with outliers problem. Notably, for λ-UFL, where β = 2 and the discrete version is NP-hard to approximate within a factor of 1.27, we describe a 2.32-approximation for the continuous version, and indeed 2.32 < 2 × 1.27. Also, for k-means, where β = 4 and the best known approximation factor for the discrete version is 9, we obtain a 32-approximation for the continuous version, which is better than 4 × 9 = 36. The main challenge one faces is that most algorithms for the discrete clustering problems, including the state of the art solutions, depend on Linear Program (LP) relaxations that become infinite-sized in the continuous version. To overcome this, we design new linear program relaxations for the continuous clustering problems which, although having exponentially many constraints, are amenable to the round-or-cut framework.
Cite as

Deeparnab Chakrabarty, Maryam Negahbani, and Ankita Sarkar. Approximation Algorithms for Continuous Clustering and Facility Location Problems. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakrabarty_et_al:LIPIcs.ESA.2022.33,
  author =	{Chakrabarty, Deeparnab and Negahbani, Maryam and Sarkar, Ankita},
  title =	{{Approximation Algorithms for Continuous Clustering and Facility Location Problems}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.33},
  URN =		{urn:nbn:de:0030-drops-169710},
  doi =		{10.4230/LIPIcs.ESA.2022.33},
  annote =	{Keywords: Approximation Algorithms, Clustering, Facility Location, Fairness, Outliers}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.21
Revisiting Priority k-Center: Fairness and Outliers

Authors: Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, and Maryam Negahbani

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In the Priority k-Center problem, the input consists of a metric space (X,d), an integer k and for each point v ∈ X a priority radius r(v). The goal is to choose k-centers S ⊆ X to minimize max_{v ∈ X} 1/(r(v)) d(v,S). If all r(v)’s were uniform, one obtains the classical k-center problem. Plesník [Ján Plesník, 1987] introduced this problem and gave a 2-approximation algorithm matching the best possible algorithm for vanilla k-center. We show how the Priority k-Center problem is related to two different notions of fair clustering [Harris et al., 2019; Christopher Jung et al., 2020]. Motivated by these developments we revisit the problem and, in our main technical contribution, develop a framework that yields constant factor approximation algorithms for Priority k-Center with outliers. Our framework extends to generalizations of Priority k-Center to matroid and knapsack constraints, and as a corollary, also yields algorithms with fairness guarantees in the lottery model of Harris et al.
Cite as

Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, and Maryam Negahbani. Revisiting Priority k-Center: Fairness and Outliers. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bajpai_et_al:LIPIcs.ICALP.2021.21,
  author =	{Bajpai, Tanvi and Chakrabarty, Deeparnab and Chekuri, Chandra and Negahbani, Maryam},
  title =	{{Revisiting Priority k-Center: Fairness and Outliers}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.21},
  URN =		{urn:nbn:de:0030-drops-140909},
  doi =		{10.4230/LIPIcs.ICALP.2021.21},
  annote =	{Keywords: Fairness, Clustering, Approximation, Outliers}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.20
Small Space Stream Summary for Matroid Center

Authors: Sagar Kale

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

Abstract
In the matroid center problem, which generalizes the k-center problem, we need to pick a set of centers that is an independent set of a matroid with rank r. We study this problem in streaming, where elements of the ground set arrive in the stream. We first show that any randomized one-pass streaming algorithm that computes a better than Delta-approximation for partition-matroid center must use Omega(r^2) bits of space, where Delta is the aspect ratio of the metric and can be arbitrarily large. This shows a quadratic separation between matroid center and k-center, for which the Doubling algorithm [Charikar et al., 1997] gives an 8-approximation using O(k)-space and one pass. To complement this, we give a one-pass algorithm for matroid center that stores at most O(r^2 log(1/epsilon)/epsilon) points (viz., stream summary) among which a (7+epsilon)-approximate solution exists, which can be found by brute force, or a (17+epsilon)-approximation can be found with an efficient algorithm. If we are allowed a second pass, we can compute a (3+epsilon)-approximation efficiently. We also consider the problem of matroid center with z outliers and give a one-pass algorithm that outputs a set of O((r^2+rz)log(1/epsilon)/epsilon) points that contains a (15+epsilon)-approximate solution. Our techniques extend to knapsack center and knapsack center with z outliers in a straightforward way, and we get algorithms that use space linear in the size of a largest feasible set (as opposed to quadratic space for matroid center).
Cite as

Sagar Kale. Small Space Stream Summary for Matroid Center. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kale:LIPIcs.APPROX-RANDOM.2019.20,
  author =	{Kale, Sagar},
  title =	{{Small Space Stream Summary for Matroid Center}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{20:1--20:22},
  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.2019.20},
  URN =		{urn:nbn:de:0030-drops-112359},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.20},
  annote =	{Keywords: Streaming Algorithms, Matroids, Clustering}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.30
Generalized Center Problems with Outliers

Authors: Deeparnab Chakrabarty and Maryam Negahbani

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

Abstract
We study the F-center problem with outliers: given a metric space (X,d), a general down-closed family F of subsets of X, and a parameter m, we need to locate a subset S in F of centers such that the maximum distance among the closest m points in X to S is minimized. Our main result is a dichotomy theorem. Colloquially, we prove that there is an efficient 3-approximation for the F-center problem with outliers if and only if we can efficiently optimize a poly-bounded linear function over F subject to a partition constraint. One concrete upshot of our result is a polynomial time 3-approximation for the knapsack center problem with outliers for which no (true) approximation algorithm was known.
Cite as

Deeparnab Chakrabarty and Maryam Negahbani. Generalized Center Problems with Outliers. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chakrabarty_et_al:LIPIcs.ICALP.2018.30,
  author =	{Chakrabarty, Deeparnab and Negahbani, Maryam},
  title =	{{Generalized Center Problems with Outliers}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{30:1--30:14},
  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.2018.30},
  URN =		{urn:nbn:de:0030-drops-90345},
  doi =		{10.4230/LIPIcs.ICALP.2018.30},
  annote =	{Keywords: Approximation Algorithms, Clustering, k-Center Problem}
}
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