15 Search Results for "Chlamtac, Eden"

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.DISC.2025.26
Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders

Authors: Emilio Cruciani, Sebastian Forster, and Tijn de Vos

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We study a multi-call variant of the classic PUSH&PULL rumor spreading process where nodes can contact k of their neighbors instead of a single one during both PUSH and PULL operations. We show that rumor spreading can be made faster at the cost of an increased amount of communication between the nodes. As a motivating example, consider the process on a complete graph of n nodes: while the standard PUSH&PULL protocol takes Θ(log n) rounds, we prove that our k-PUSH&PULL variant completes in Θ(log_{k} n) rounds, with high probability. We generalize this result in an expansion-sensitive way, as has been done for the classic PUSH&PULL protocol for different notions of expansion, e.g., conductance and vertex expansion. We consider small-set vertex expanders, graphs in which every sufficiently small subset of nodes has a large neighborhood, ensuring strong local connectivity. In particular, when the expansion parameter satisfies ϕ > 1, these graphs have a diameter of o(log n), as opposed to other standard notions of expansion. Since the graph’s diameter is a lower bound on the number of rounds required for rumor spreading, this makes small-set expanders particularly well-suited for fast information dissemination. We prove that k-PUSH&PULL takes O(log_{ϕ} n ⋅ log_{k} n) rounds in these expanders, with high probability. We complement this with a simple lower bound of Ω(log_{ϕ} n+ log_{k} n) rounds.
Cite as

Emilio Cruciani, Sebastian Forster, and Tijn de Vos. Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 26:1-26:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cruciani_et_al:LIPIcs.DISC.2025.26,
  author =	{Cruciani, Emilio and Forster, Sebastian and de Vos, Tijn},
  title =	{{Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{26:1--26:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.26},
  URN =		{urn:nbn:de:0030-drops-248434},
  doi =		{10.4230/LIPIcs.DISC.2025.26},
  annote =	{Keywords: small set expansion, vertex expansion, rumor spreading, multi-call rumor spreading, push\&pull protocol}
}
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.2025.22
Directed Buy-At-Bulk Spanners

Authors: Elena Grigorescu, Nithish Kumar, and Young-San Lin

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

Abstract
We present a framework that unifies directed buy-at-bulk network design and directed spanner problems, namely, buy-at-bulk spanners. The goal is to find a minimum-cost routing solution for network design problems that captures economies at scale, while satisfying demands and distance constraints for terminal pairs. A more restricted version of this problem was shown to be O(2^{log^{1-ε} n})-hard to approximate, where n is the number of vertices, under a standard complexity assumption, by Elkin and Peleg (Theory of Computing Systems, 2007). Our results for buy-at-bulk spanners are the following. - When the edge lengths are integral with magnitude polynomial in n we present: 1) An Õ(n^{4/5 + ε})-approximation polynomial-time randomized algorithm for uniform demands. 2) An Õ(k^{1/2 + ε})-approximation polynomial-time randomized algorithm for general demands, where k is the number of terminal pairs. This can be improved to an Õ(k^{ε})-approximation algorithm for the single-source problem. The same approximation ratios hold in the online setting. - When the edge lengths are rational and well-conditioned, we present an Õ(k^{1/2 + ε})-approximation polynomial-time randomized algorithm that may slightly violate the distance constraints. The result can be improved to an Õ(k^ε)-approximation algorithm for the single-source problem. The same approximation ratios hold for the online setting when the condition number is given in advance. To the best of our knowledge, these are the first sublinear factor approximation algorithms for directed buy-at-bulk spanners. We allow the edge lengths to be negative and the demands to be non-unit, unlike the previous literature. Our approximation ratios match the state-of-the-art ratios in special cases, namely, buy-at-bulk network design by Antonakopoulos (WAOA, 2010) and (online) weighted spanners by Grigorescu, Kumar, and Lin (APPROX 2023). Furthermore, we improve the competitive ratio for online buy-at-bulk by Chakrabarty, Ene, Krishnaswamy, and Panigrahi (SICOMP, 2018) by a factor of log R, where R is the ratio between the maximum demand and the minimum demand.
Cite as

Elena Grigorescu, Nithish Kumar, and Young-San Lin. Directed Buy-At-Bulk Spanners. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 22:1-22:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grigorescu_et_al:LIPIcs.APPROX/RANDOM.2025.22,
  author =	{Grigorescu, Elena and Kumar, Nithish and Lin, Young-San},
  title =	{{Directed Buy-At-Bulk Spanners}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{22:1--22:24},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-243885},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.22},
  annote =	{Keywords: buy-at-bulk spanners, minimum density junction tree, resource constrained shortest path}
}
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.50
New Results on a General Class of Minimum Norm Optimization Problems

Authors: Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang

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

Abstract
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set 𝒰 of n weighted elements and a family of feasible subsets ℱ. Each subset S ∈ ℱ is called a feasible solution/set of the problem. We denote the value vector by v = {v_i}_{i ∈ [n]}, where v_i ≥ 0 is the value of element i. For any subset S ⊆ 𝒰, we use v[S] to denote the n-dimensional vector {v_e⋅ 𝟏[e ∈ S]}_{e ∈ 𝒰} (i.e., we zero out all entries that are not in S). Let f: ℝⁿ → ℝ_+ be a symmetric monotone norm function. Our goal is to minimize the norm objective f(v[S]) over feasible subset S ∈ ℱ. The problem significantly generalizes the corresponding min-sum and min-max problems. We present a general equivalent reduction of the norm minimization problem to a multi-criteria optimization problem with logarithmic budget constraints, up to a constant approximation factor. Leveraging this reduction, we obtain constant factor approximation algorithms for the norm minimization versions of several covering problems, such as interval cover, multi-dimensional knapsack cover, and logarithmic factor approximation for set cover. We also study the norm minimization versions for perfect matching, s-t path and s-t cut. We show the natural linear programming relaxations for these problems have a large integrality gap. To complement the negative result, we show that, for perfect matching, it is possible to obtain a bi-criteria result: for any constant ε,δ > 0, we can find in polynomial time a nearly perfect matching (i.e., a matching that matches at least 1-ε proportion of vertices) and its cost is at most (8+δ) times of the optimum for perfect matching. Moreover, we establish the existence of a polynomial-time O(log log n)-approximation algorithm for the norm minimization variant of the s-t path problem. Specifically, our algorithm achieves an α-approximation with a time complexity of n^{O(log log n / α)}, where 9 ≤ α ≤ log log n.
Cite as

Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang. New Results on a General Class of Minimum Norm Optimization Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.50,
  author =	{Chen, Kuowen and Li, Jian and Rabani, Yuval and Zhang, Yiran},
  title =	{{New Results on a General Class of Minimum Norm Optimization Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{50:1--50:20},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-234276},
  doi =		{10.4230/LIPIcs.ICALP.2025.50},
  annote =	{Keywords: Approximation Algorithms, Minimum Norm Optimization, Linear Programming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

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

Abstract
For a given graph G, a hopset H with hopbound β and stretch α is a set of edges such that between every pair of vertices u and v, there is a path with at most β hops in G ∪ H that approximates the distance between u and v up to a multiplicative stretch of α. Hopsets have found a wide range of applications for distance-based problems in various computational models since the 90s. More recently, there has been significant interest in understanding these fundamental objects from an existential and structural perspective. But all of this work takes a worst-case (or existential) point of view: How many edges do we need to add to satisfy a given hopbound and stretch requirement for any input graph? We initiate the study of the natural optimization variant of this problem: given a specific graph instance, what is the minimum number of edges that satisfy the hopbound and stretch requirements? We give approximation algorithms for a generalized hopset problem which, when combined with known existential bounds, lead to different approximation guarantees for various regimes depending on hopbound, stretch, and directed vs. undirected inputs. We complement our upper bounds with a lower bound that implies Label Cover hardness for directed hopsets and shortcut sets with hopbound at least 3.
Cite as

Michael Dinitz, Ama Koranteng, and Yasamin Nazari. Approximation Algorithms for Optimal Hopsets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.21
Targeted Least Cardinality Candidate Key for Relational Databases

Authors: Vasileios Nakos, Hung Q. Ngo, and Charalampos E. Tsourakakis

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Functional dependencies (FDs) are a central theme in databases, playing a major role in the design of database schemas and the optimization of queries [Ramakrishnan and Gehrke, 2003]. In this work, we introduce the targeted least cardinality candidate key problem (TCAND). This problem is defined over a set of functional dependencies ℱ and a target variable set T ⊆ V, and it aims to find the smallest set X ⊆ V such that the FD X → T can be derived from ℱ. The TCAND problem generalizes the well-known NP-hard problem of finding the least cardinality candidate key [Lucchesi and Osborn, 1978], which has been previously demonstrated to be at least as difficult as the set cover problem. We present an integer programming (IP) formulation for the TCAND problem, analogous to a layered set cover problem. We analyze its linear programming (LP) relaxation from two perspectives: we propose two approximation algorithms and investigate the integrality gap. Our findings indicate that the approximation upper bounds for our algorithms are not significantly improvable through LP rounding, a notable distinction from the standard Set Cover problem. Additionally, we discover that a generalization of the TCAND problem is equivalent to a variant of the Set Cover problem, named Red Blue Set Cover [Carr et al., 2000], which cannot be approximated within a sub-polynomial factor in polynomial time under plausible conjectures [Chlamtáč et al., 2023]. Despite the extensive history surrounding the issue of identifying the least cardinality candidate key, our research contributes new theoretical insights, novel algorithms, and demonstrates that the general TCAND problem poses complexities beyond those encountered in the Set Cover problem.
Cite as

Vasileios Nakos, Hung Q. Ngo, and Charalampos E. Tsourakakis. Targeted Least Cardinality Candidate Key for Relational Databases. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nakos_et_al:LIPIcs.ICDT.2025.21,
  author =	{Nakos, Vasileios and Ngo, Hung Q. and Tsourakakis, Charalampos E.},
  title =	{{Targeted Least Cardinality Candidate Key for Relational Databases}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.21},
  URN =		{urn:nbn:de:0030-drops-229628},
  doi =		{10.4230/LIPIcs.ICDT.2025.21},
  annote =	{Keywords: functional dependencies, candidate key, approximation algorithms, hardness}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.11
Approximating Red-Blue Set Cover and Minimum Monotone Satisfying Assignment

Authors: Eden Chlamtáč, Yury Makarychev, and Ali Vakilian

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We provide new approximation algorithms for the Red-Blue Set Cover and Circuit Minimum Monotone Satisfying Assignment (MMSA) problems. Our algorithm for Red-Blue Set Cover achieves Õ(m^{1/3})-approximation improving on the Õ(m^{1/2})-approximation due to Elkin and Peleg (where m is the number of sets). Our approximation algorithm for MMSA_t (for circuits of depth t) gives an Õ(N^{1-δ}) approximation for δ = 1/32^{3-⌈t/2⌉}, where N is the number of gates and variables. No non-trivial approximation algorithms for MMSA_t with t ≥ 4 were previously known. We complement these results with lower bounds for these problems: For Red-Blue Set Cover, we provide a nearly approximation preserving reduction from Min k-Union that gives an ̃Ω(m^{1/4 - ε}) hardness under the Dense-vs-Random conjecture, while for MMSA we sketch a proof that an SDP relaxation strengthened by Sherali-Adams has an integrality gap of N^{1-ε} where ε → 0 as the circuit depth t → ∞.
Cite as

Eden Chlamtáč, Yury Makarychev, and Ali Vakilian. Approximating Red-Blue Set Cover and Minimum Monotone Satisfying Assignment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX/RANDOM.2023.11,
  author =	{Chlamt\'{a}\v{c}, Eden and Makarychev, Yury and Vakilian, Ali},
  title =	{{Approximating Red-Blue Set Cover and Minimum Monotone Satisfying Assignment}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.11},
  URN =		{urn:nbn:de:0030-drops-188366},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.11},
  annote =	{Keywords: Red-Blue Set Cover Problem, Circuit Minimum Monotone Satisfying Assignment (MMSA) Problem, LP Rounding}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.41
How to Cut a Ball Without Separating: Improved Approximations for Length Bounded Cut

Authors: Eden Chlamtáč and Petr Kolman

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
The Minimum Length Bounded Cut problem is a natural variant of Minimum Cut: given a graph, terminal nodes s,t and a parameter L, find a minimum cardinality set of nodes (other than s,t) whose removal ensures that the distance from s to t is greater than L. We focus on the approximability of the problem for bounded values of the parameter L. The problem is solvable in polynomial time for L ≤ 4 and NP-hard for L ≥ 5. The best known algorithms have approximation factor ⌈ (L-1)/2⌉. It is NP-hard to approximate the problem within a factor of 1.17175 and Unique Games hard to approximate it within Ω(L), for any L ≥ 5. Moreover, for L = 5 the problem is 4/3-ε Unique Games hard for any ε > 0. Our first result matches the hardness for L = 5 with a 4/3-approximation algorithm for this case, improving over the previous 2-approximation. For 6-bounded cuts we give a 7/4-approximation, improving over the previous best 3-approximation. More generally, we achieve approximation ratios that always outperform the previous ⌈ (L-1)/2⌉ guarantee for any (fixed) value of L, while for large values of L, we achieve a significantly better ((11/25)L+O(1))-approximation. All our algorithms apply in the weighted setting, in both directed and undirected graphs, as well as for edge-cuts, which easily reduce to the node-cut variant. Moreover, by rounding the natural linear programming relaxation, our algorithms also bound the corresponding bounded-length flow-cut gaps.
Cite as

Eden Chlamtáč and Petr Kolman. How to Cut a Ball Without Separating: Improved Approximations for Length Bounded Cut. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX/RANDOM.2020.41,
  author =	{Chlamt\'{a}\v{c}, Eden and Kolman, Petr},
  title =	{{How to Cut a Ball Without Separating: Improved Approximations for Length Bounded Cut}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.41},
  URN =		{urn:nbn:de:0030-drops-126446},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.41},
  annote =	{Keywords: Approximation Algorithms, Length Bounded Cuts, Cut-Flow Duality, Rounding of Linear Programms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.11
Approximating the Norms of Graph Spanners

Authors: Eden Chlamtáč, Michael Dinitz, and Thomas Robinson

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

Abstract
The l_p-norm of the degree vector was recently introduced by [Chlamtáč, Dinitz, Robinson ICALP '19] as a new cost metric for graph spanners, as it interpolates between two traditional notions of cost (the sparsity l_1 and the max degree l_infty) and is well-motivated from applications. We study this from an approximation algorithms point of view, analyzing old algorithms and designing new algorithms for this new context, as well as providing hardness results. Our main results are for the l_2-norm and stretch 3, where we give a tight analysis of the greedy algorithm and a new algorithm specifically tailored to this setting which gives an improved approximation ratio.
Cite as

Eden Chlamtáč, Michael Dinitz, and Thomas Robinson. Approximating the Norms of Graph Spanners. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2019.11,
  author =	{Chlamt\'{a}\v{c}, Eden and Dinitz, Michael and Robinson, Thomas},
  title =	{{Approximating the Norms of Graph Spanners}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{11:1--11:22},
  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.2019.11},
  URN =		{urn:nbn:de:0030-drops-112261},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.11},
  annote =	{Keywords: Spanners, Approximations}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.40
The Norms of Graph Spanners

Authors: Eden Chlamtáč, Michael Dinitz, and Thomas Robinson

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
A t-spanner of a graph G is a subgraph H in which all distances are preserved up to a multiplicative t factor. A classical result of Althöfer et al. is that for every integer k and every graph G, there is a (2k-1)-spanner of G with at most O(n^{1+1/k}) edges. But for some settings the more interesting notion is not the number of edges, but the degrees of the nodes. This spurred interest in and study of spanners with small maximum degree. However, this is not necessarily a robust enough objective: we would like spanners that not only have small maximum degree, but also have "few" nodes of "large" degree. To interpolate between these two extremes, in this paper we initiate the study of graph spanners with respect to the l_p-norm of their degree vector, thus simultaneously modeling the number of edges (the l_1-norm) and the maximum degree (the l_{infty}-norm). We give precise upper bounds for all ranges of p and stretch t: we prove that the greedy (2k-1)-spanner has l_p norm of at most max(O(n), O(n^{{k+p}/{kp}})), and that this bound is tight (assuming the Erdős girth conjecture). We also study universal lower bounds, allowing us to give "generic" guarantees on the approximation ratio of the greedy algorithm which generalize and interpolate between the known approximations for the l_1 and l_{infty} norm. Finally, we show that at least in some situations, the l_p norm behaves fundamentally differently from l_1 or l_{infty}: there are regimes (p=2 and stretch 3 in particular) where the greedy spanner has a provably superior approximation to the generic guarantee.
Cite as

Eden Chlamtáč, Michael Dinitz, and Thomas Robinson. The Norms of Graph Spanners. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chlamtac_et_al:LIPIcs.ICALP.2019.40,
  author =	{Chlamt\'{a}\v{c}, Eden and Dinitz, Michael and Robinson, Thomas},
  title =	{{The Norms of Graph Spanners}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.40},
  URN =		{urn:nbn:de:0030-drops-106163},
  doi =		{10.4230/LIPIcs.ICALP.2019.40},
  annote =	{Keywords: spanners, approximations}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.10
Sherali-Adams Integrality Gaps Matching the Log-Density Threshold

Authors: Eden Chlamtác and Pasin Manurangsi

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-k-Subgraph and Small Set Bipartite Vertex Expansion. These approximations have been conjectured to be optimal based on various instantiations of a general conjecture: that it is hard to distinguish a fully random combinatorial structure from one which contains a similar planted sub-structure with the same "log-density". We bolster this conjecture by showing that in a random hypergraph with edge probability n^{-alpha}, Omega(log n) rounds of Sherali-Adams cannot rule out the existence of a k-subhypergraph with edge density k^{-alpha-o(1)}, for any k and alpha. This holds even when the bound on the objective function is lifted. This gives strong integrality gaps which exactly match the gap in the above distinguishing problems, as well as the best-known approximations, for Densest k-Subgraph, Smallest p-Edge Subgraph, their hypergraph extensions, and Small Set Bipartite Vertex Expansion (or equivalently, Minimum p-Union). Previously, such integrality gaps were known only for Densest k-Subgraph for one specific parameter setting.
Cite as

Eden Chlamtác and Pasin Manurangsi. Sherali-Adams Integrality Gaps Matching the Log-Density Threshold. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2018.10,
  author =	{Chlamt\'{a}c, Eden and Manurangsi, Pasin},
  title =	{{Sherali-Adams Integrality Gaps Matching the Log-Density Threshold}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.10},
  URN =		{urn:nbn:de:0030-drops-94142},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.10},
  annote =	{Keywords: Approximation algorithms, integrality gaps, lift-and-project, log-density, Densest k-Subgraph}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.6
The Densest k-Subhypergraph Problem

Authors: Eden Chlamtac, Michael Dinitz, Christian Konrad, Guy Kortsarz, and George Rabanca

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
The Densest k-Subgraph (DkS) problem, and its corresponding minimization problem Smallest p-Edge Subgraph (SpES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed that they do not an admit a subpolynomial approximation ratio (although the best known hardness results do not rule this out). In this paper we generalize both DkS and SpES from graphs to hypergraphs. We consider the Densest k-Subhypergraph problem (given a hypergraph (V, E), find a subset W subseteq V of k vertices so as to maximize the number of hyperedges contained in W) and define the Minimum p-Union problem (given a hypergraph, choose p of the hyperedges so as to minimize the number of vertices in their union). We focus in particular on the case where all hyperedges have size 3, as this is the simplest non-graph setting. For this case we provide an O(n^{4(4-sqrt{3})/13 + epsilon}) <= O(n^{0.697831+epsilon})-approximation (for arbitrary constant epsilon > 0) for Densest k-Subhypergraph and an ~O(n^{2/5})-approximation for Minimum p-Union. We also give an O(sqrt{m})-approximation for Minimum p-Union in general hypergraphs. Finally, we examine the interesting special case of interval hypergraphs (instances where the vertices are a subset of the natural numbers and the hyperedges are intervals of the line) and prove that both problems admit an exact polynomial time solution on these instances.
Cite as

Eden Chlamtac, Michael Dinitz, Christian Konrad, Guy Kortsarz, and George Rabanca. The Densest k-Subhypergraph Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2016.6,
  author =	{Chlamtac, Eden and Dinitz, Michael and Konrad, Christian and Kortsarz, Guy and Rabanca, George},
  title =	{{The Densest k-Subhypergraph Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.6},
  URN =		{urn:nbn:de:0030-drops-66298},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.6},
  annote =	{Keywords: Hypergraphs, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.80
Lowest Degree k-Spanner: Approximation and Hardness

Authors: Eden Chlamtác and Michael Dinitz

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
A k-spanner is a subgraph in which distances are approximately preserved, up to some given stretch factor k. We focus on the following problem: Given a graph and a value k, can we find a k-spanner that minimizes the maximum degree? While reasonably strong bounds are known for some spanner problems, they almost all involve minimizing the total number of edges. Switching the objective to the degree introduces significant new challenges, and currently the only known approximation bound is an O~(Delta^(3-2*sqrt(2)))-approximation for the special case when k = 2 [Chlamtac, Dinitz, Krauthgamer FOCS 2012] (where Delta is the maximum degree in the input graph). In this paper we give the first non-trivial algorithm and polynomial-factor hardness of approximation for the case of general k. Specifically, we give an LP-based O~(Delta^((1-1/k)^2) )-approximation and prove that it is hard to approximate the optimum to within Delta^Omega(1/k) when the graph is undirected, and to within Delta^Omega(1) when it is directed.
Cite as

Eden Chlamtác and Michael Dinitz. Lowest Degree k-Spanner: Approximation and Hardness. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 80-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2014.80,
  author =	{Chlamt\'{a}c, Eden and Dinitz, Michael},
  title =	{{Lowest Degree k-Spanner: Approximation and Hardness}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{80--95},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.80},
  URN =		{urn:nbn:de:0030-drops-46894},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.80},
  annote =	{Keywords: Graph spanners, approximation algorithms, hardness of approximation}
}
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