22 Search Results for "Norouzi-Fard, Ashkan"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.34
Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces

Authors: Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn

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

Abstract
The k-median and k-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the k-median (resp. k-means) problem is to find k representative points so as to minimize the sum of the distances (resp. sum of squared distances) from each point to its closest representative. Cohen-Addad, Feldmann, and Saulpic [JACM'21] showed how to obtain a (1+ε)-factor approximation in low-dimensional Euclidean metric for both the k-median and k-means problems in near-linear time 2^{(1/ε)^O(d²)} n ⋅ polylog(n) (where d is the dimension and n is the number of input points). We improve this running time to 2^{O(1/ε)^{d-1}} ⋅ n ⋅ polylog(n), and show an almost matching lower bound: under the Gap Exponential Time Hypothesis for 3-SAT, there is no 2^o(1/ε^{d-1}) n^O(1) algorithm achieving a (1+ε)-approximation for k-means.
Cite as

Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn. Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohenaddad_et_al:LIPIcs.SoCG.2026.34,
  author =	{Cohen-Addad, Vincent and Karthik C. S. and Saulpic, David and Schwiegelshohn, Chris},
  title =	{{Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.34},
  URN =		{urn:nbn:de:0030-drops-258404},
  doi =		{10.4230/LIPIcs.SoCG.2026.34},
  annote =	{Keywords: k-means clustering, k-median clustering, Euclidean space, Fine-Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.105
Fixed-Parameter Tractable Submodular Maximization over a Matroid

Authors: Shamisa Nematollahi, Adrian Vladu, and Junyao Zhao

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

Abstract
In this paper, we design fixed-parameter tractable (FPT) algorithms for (non-monotone) submodular maximization subject to a matroid constraint, where the matroid rank r is treated as a fixed parameter that is independent of the total number of elements n. We provide two FPT algorithms: one for the offline setting and another for the random-order streaming setting. Our streaming algorithm achieves a 1/2-ε approximation using Õ(r/poly(ε)) memory, while our offline algorithm obtains a 1-(1)/(e)-ε approximation with n⋅ 2^{Õ(r/poly(ε))} runtime and Õ(r/poly(ε)) memory. Both approximation factors are near-optimal in their respective settings, given existing hardness results. In particular, our offline algorithm demonstrates that - unlike in the polynomial-time regime - there is essentially no separation between monotone and non-monotone submodular maximization under a matroid constraint in the FPT framework.
Cite as

Shamisa Nematollahi, Adrian Vladu, and Junyao Zhao. Fixed-Parameter Tractable Submodular Maximization over a Matroid. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 105:1-105:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{nematollahi_et_al:LIPIcs.ITCS.2026.105,
  author =	{Nematollahi, Shamisa and Vladu, Adrian and Zhao, Junyao},
  title =	{{Fixed-Parameter Tractable Submodular Maximization over a Matroid}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{105:1--105:22},
  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.2026.105},
  URN =		{urn:nbn:de:0030-drops-253924},
  doi =		{10.4230/LIPIcs.ITCS.2026.105},
  annote =	{Keywords: Submodular maximization, matroids, parameterized complexity, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.67
Query Lower Bounds for Correlation Clustering Under Memory Constraints

Authors: Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou

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

Abstract
This work initiates the study of memory–query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non‑edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of ε n², any algorithm requires Ω(n/ε²) adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make ≫ n/ε² adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.
Cite as

Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou. Query Lower Bounds for Correlation Clustering Under Memory Constraints. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{garg_et_al:LIPIcs.ITCS.2026.67,
  author =	{Garg, Sumegha and He, Songhua and Papakonstantinou, Periklis A.},
  title =	{{Query Lower Bounds for Correlation Clustering Under Memory Constraints}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{67:1--67:24},
  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.2026.67},
  URN =		{urn:nbn:de:0030-drops-253542},
  doi =		{10.4230/LIPIcs.ITCS.2026.67},
  annote =	{Keywords: correlation clustering, query-space complexity, information theory}
}
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.2025.41
Min-Max Correlation Clustering via Neighborhood Similarity

Authors: Nairen Cao, Steven Roche, and Hsin-Hao Su

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

Abstract
We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive (+) or negative (-), and the objective is to find a clustering that minimizes the 𝓁_∞-norm of the disagreement vector over all vertices. We address this problem with an efficient (3 + ε)-approximation algorithm that runs in nearly linear time, Õ(|E^+|), where |E^+| denotes the number of positive edges. This improves upon the previous best-known approximation guarantee of 4 by Heidrich, Irmai, and Andres [Heidrich et al., 2024], whose algorithm runs in O(|V|² + |V| D²) time, where |V| is the number of nodes and D is the maximum degree in the graph (V,E^+). Furthermore, we extend our algorithm to the massively parallel computation (MPC) model and the semi-streaming model. In the MPC model, our algorithm runs on machines with memory sublinear in the number of nodes and takes O(1) rounds. In the streaming model, our algorithm requires only Õ(|V|) space, where |V| is the number of vertices in the graph. Our algorithms are purely combinatorial. They are based on a novel structural observation about the optimal min-max instance, which enables the construction of a (3 + ε)-approximation algorithm using O(|E^+|) neighborhood similarity queries. By leveraging random projection, we further show these queries can be computed in nearly linear time.
Cite as

Nairen Cao, Steven Roche, and Hsin-Hao Su. Min-Max Correlation Clustering via Neighborhood Similarity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 41:1-41:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cao_et_al:LIPIcs.ESA.2025.41,
  author =	{Cao, Nairen and Roche, Steven and Su, Hsin-Hao},
  title =	{{Min-Max Correlation Clustering via Neighborhood Similarity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{41:1--41:18},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-245098},
  doi =		{10.4230/LIPIcs.ESA.2025.41},
  annote =	{Keywords: Min Max Correlation Clustering, Approximate algorithms}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.33
A Min-Entropy Approach to Multi-Party Communication Lower Bounds

Authors: Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Information complexity is one of the most powerful techniques to prove information-theoretical lower bounds, in which Shannon entropy plays a central role. Though Shannon entropy has some convenient properties, such as the chain rule, it still has inherent limitations. One of the most notable barriers is the square-root loss, which appears in the square-root gap between entropy gaps and statistical distances, e.g., Pinsker’s inequality. To bypass this barrier, we introduce a new method based on min-entropy analysis. Building on this new method, we prove the following results. - An Ω(N^{∑_i α_i - max_i {α_i}}/k) randomized communication lower bound of the k-party set-intersection problem where the i-th party holds a random set of size ≈ N^{1-α_i}. - A tight Ω(n/k) randomized lower bound of the k-party Tree Pointer Jumping problems, improving an Ω(n/k²) lower bound by Chakrabarti, Cormode, and McGregor (STOC 08). - An Ω(n/k+√n) lower bound of the Chained Index problem, improving an Ω(n/k²) lower bound by Cormode, Dark, and Konrad (ICALP 19). Since these problems served as hard problems for numerous applications in streaming lower bounds and cryptography, our new lower bounds directly improve these streaming lower bounds and cryptography lower bounds. On the technical side, min-entropy does not have nice properties such as the chain rule. To address this issue, we enhance the structure-vs-pseudorandomness decomposition used by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24); both papers used this decomposition to prove communication lower bounds. In this paper, we give a new breath to this method in the multi-party setting, presenting a new toolkit for proving multi-party communication lower bounds.
Cite as

Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang. A Min-Entropy Approach to Multi-Party Communication Lower Bounds. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 33:1-33:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.CCC.2025.33,
  author =	{Huang, Mi-Ying (Miryam) and Mao, Xinyu and Wang, Shuo and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{A Min-Entropy Approach to Multi-Party Communication Lower Bounds}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{33:1--33:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.33},
  URN =		{urn:nbn:de:0030-drops-237273},
  doi =		{10.4230/LIPIcs.CCC.2025.33},
  annote =	{Keywords: communication complexity, lifting theorems, set intersection, chained index}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.19
Dynamic Algorithms for Submodular Matching

Authors: Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh

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

Abstract
The Maximum Submodular Matching (MSM) problem is a generalization of the classical Maximum Weight Matching (MWM) problem. In this problem, given a monotone submodular function f: 2^E → ℝ^{≥ 0} defined over subsets of edges of a graph G(V, E), we are asked to return a matching whose submodular value is maximum among all matchings in graph G(V, E). In this paper, we consider this problem in a fully dynamic setting against an oblivious adversary. In this setting, we are given a sequence 𝒮 of insertions and deletions of edges of the underlying graph G(V, E), along with an oracle access to the monotone submodular function f. The goal is to maintain a matching M such that, at any time t of sequence 𝒮, its submodular value is a good approximation of the value of the optimal submodular matching while keeping the number of operations minimal. We develop the first dynamic algorithm for the submodular matching problem, in which we maintain a matching whose submodular value is within expected (8 + ε)-approximation of the optimal submodular matching at any time t of sequence 𝒮 using expected amortized poly(log n, 1/(ε)) update time. Our approach incorporates a range of novel techniques, notably the concept of Uniform Hierarchical Caches (UHC) data structure along with its invariants, which lead to the first algorithm for fully dynamic submodular matching and may be of independent interest for designing dynamic algorithms for other problems.
Cite as

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh. Dynamic Algorithms for Submodular Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ICALP.2025.19,
  author =	{Banihashem, Kiarash and Biabani, Leyla and Goudarzi, Samira and Hajiaghayi, MohammadTaghi and Jabbarzade, Peyman and Monemizadeh, Morteza},
  title =	{{Dynamic Algorithms for Submodular Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-233969},
  doi =		{10.4230/LIPIcs.ICALP.2025.19},
  annote =	{Keywords: Matching, Submodular, Dynamic, Polylogarithmic}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.64
Fully Scalable MPC Algorithms for Euclidean k-Center

Authors: Artur Czumaj, Guichen Gao, Mohsen Ghaffari, and Shaofeng H.-C. Jiang

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

Abstract
The k-center problem is a fundamental optimization problem with numerous applications in machine learning, data analysis, data mining, and communication networks. The k-center problem has been extensively studied in the classical sequential setting for several decades, and more recently there have been some efforts in understanding the problem in parallel computing, on the Massively Parallel Computation (MPC) model. For now, we have a good understanding of k-center in the case where each local MPC machine has sufficient local memory to store some representatives from each cluster, that is, when one has Ω(k) local memory per machine. While this setting covers the case of small values of k, for a large number of clusters these algorithms require undesirably large local memory, making them poorly scalable. The case of large k has been considered only recently for the fully scalable low-local-memory MPC model for the Euclidean instances of the k-center problem. However, the earlier works have been considering only the constant dimensional Euclidean space, required a super-constant number of rounds, and produced only k(1+o(1)) centers whose cost is a super-constant approximation of k-center. In this work, we significantly improve upon the earlier results for the k-center problem for the fully scalable low-local-memory MPC model. In the low dimensional Euclidean case in ℝ^d, we present the first constant-round fully scalable MPC algorithm for (2+ε)-approximation. We push the ratio further to (1 + ε)-approximation albeit using slightly more (1 + ε)k centers. All these results naturally extends to slightly super-constant values of d. In the high-dimensional regime, we provide the first fully scalable MPC algorithm that in a constant number of rounds achieves an O(log n/ log log n)-approximation for k-center.
Cite as

Artur Czumaj, Guichen Gao, Mohsen Ghaffari, and Shaofeng H.-C. Jiang. Fully Scalable MPC Algorithms for Euclidean k-Center. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 64:1-64:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2025.64,
  author =	{Czumaj, Artur and Gao, Guichen and Ghaffari, Mohsen and Jiang, Shaofeng H.-C.},
  title =	{{Fully Scalable MPC Algorithms for Euclidean k-Center}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{64:1--64:20},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-234416},
  doi =		{10.4230/LIPIcs.ICALP.2025.64},
  annote =	{Keywords: Massively Parallel Computing, Euclidean Spaces, k-Center Clustering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.62
Deterministic k-Median Clustering in Near-Optimal Time

Authors: Martín Costa and Ermiya Farokhnejad

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

Abstract
The metric k-median problem is a textbook clustering problem. As input, we are given a metric space V of size n and an integer k, and our task is to find a subset S ⊆ V of at most k "centers" that minimizes the total distance from each point in V to its nearest center in S. Mettu and Plaxton [UAI'02] gave a randomized algorithm for k-median that computes a O(1)-approximation in Õ(nk) time. They also showed that any algorithm for this problem with a bounded approximation ratio must have a running time of Ω(nk). Thus, the running time of their algorithm is optimal up to polylogarithmic factors. For deterministic k-median, Guha et al. [FOCS'00] gave an algorithm that computes a poly(log (n/k))-approximation in Õ(nk) time, where the degree of the polynomial in the approximation is unspecified. To the best of our knowledge, this remains the state-of-the-art approximation of any deterministic k-median algorithm with this running time. This leads us to the following natural question: What is the best approximation of a deterministic k-median algorithm with near-optimal running time? We make progress in answering this question by giving a deterministic algorithm that computes a O(log(n/k))-approximation in Õ(nk) time. We also provide a lower bound showing that any deterministic algorithm with this running time must have an approximation ratio of Ω(log n/(log k + log log n)), establishing a gap between the randomized and deterministic settings for k-median.
Cite as

Martín Costa and Ermiya Farokhnejad. Deterministic k-Median Clustering in Near-Optimal Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 62:1-62:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{costa_et_al:LIPIcs.ICALP.2025.62,
  author =	{Costa, Mart{\'\i}n and Farokhnejad, Ermiya},
  title =	{{Deterministic k-Median Clustering in Near-Optimal Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{62:1--62:20},
  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.2025.62},
  URN =		{urn:nbn:de:0030-drops-234395},
  doi =		{10.4230/LIPIcs.ICALP.2025.62},
  annote =	{Keywords: k-clustering, k-median, deterministic algorithms, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.119
Faster Semi-Streaming Matchings via Alternating Trees

Authors: Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu

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

Abstract
We design a deterministic algorithm for the (1+ε)-approximate maximum matching problem. Our primary result demonstrates that this problem can be solved in O(ε^{-6}) semi-streaming passes, improving upon the O(ε^{-19}) pass-complexity algorithm by [Fischer, Mitrović, and Uitto, STOC'22]. This contributes substantially toward resolving Open question 2 from [Assadi, SOSA'24]. Leveraging the framework introduced in [FMU'22], our algorithm achieves an analogous round complexity speed-up for computing a (1+ε)-approximate maximum matching in both the Massively Parallel Computation (MPC) and CONGEST models. The data structures maintained by our algorithm are formulated using blossom notation and represented through alternating trees. This approach enables a simplified correctness analysis by treating specific components as if operating on bipartite graphs, effectively circumventing certain technical intricacies present in prior work.
Cite as

Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu. Faster Semi-Streaming Matchings via Alternating Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 119:1-119:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mitrovic_et_al:LIPIcs.ICALP.2025.119,
  author =	{Mitrovi\'{c}, Slobodan and Mukherjee, Anish and Sankowski, Piotr and Sheu, Wen-Horng},
  title =	{{Faster Semi-Streaming Matchings via Alternating Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{119:1--119:19},
  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.2025.119},
  URN =		{urn:nbn:de:0030-drops-234965},
  doi =		{10.4230/LIPIcs.ICALP.2025.119},
  annote =	{Keywords: streaming algorithms, approximation algorithms, maximum matching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.116
A 0.51-Approximation of Maximum Matching in Sublinear n^{1.5} Time

Authors: Sepideh Mahabadi, Mohammad Roghani, and Jakub Tarnawski

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

Abstract
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a 0.5109-approximation algorithm with a running time of Õ(n√n). All previous algorithms either provide only a marginal improvement (e.g., 2^{-280}) over the 0.5-approximation that arises from estimating a maximal matching, or have a running time that is nearly n². Our approach is also arguably much simpler than other algorithms beating 0.5-approximation.
Cite as

Sepideh Mahabadi, Mohammad Roghani, and Jakub Tarnawski. A 0.51-Approximation of Maximum Matching in Sublinear n^{1.5} Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 116:1-116:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mahabadi_et_al:LIPIcs.ICALP.2025.116,
  author =	{Mahabadi, Sepideh and Roghani, Mohammad and Tarnawski, Jakub},
  title =	{{A 0.51-Approximation of Maximum Matching in Sublinear n^\{1.5\} Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{116:1--116:17},
  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.2025.116},
  URN =		{urn:nbn:de:0030-drops-234932},
  doi =		{10.4230/LIPIcs.ICALP.2025.116},
  annote =	{Keywords: Sublinear Algorithms, Maximum Matching, Maximal Matching, Approximation Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.42
Fitting Tree Metrics and Ultrametrics in Data Streams

Authors: Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis

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

Abstract
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Formally, given a positive distance function D: binom(V,2) → ℝ_{>0}, the goal is to find a tree (or an ultrametric) T including all elements of set V, such that the difference between the distances among vertices in T and those specified by D is minimized. Numerical taxonomy was first introduced by Sneath and Sokal [Nature 1962], and since then it has been studied extensively in both biology and computer science. In this paper, we initiate the study of ultrametric and tree metric fitting problems in the semi-streaming model, where the distances between pairs of elements from V (with |V| = n), defined by the function D, can arrive in an arbitrary order. We study these problems under various distance norms; namely the 𝓁₀ objective, which aims to minimize the number of modified entries in D to fit a tree-metric or an ultrametric; the 𝓁₁ objective, which seeks to minimize the total sum of distance errors across all pairs of points in V; and the 𝓁_∞ objective, which focuses on minimizing the maximum error incurred by any entries in D. - Our first result addresses the 𝓁₀ objective. We provide a single-pass polynomial-time Õ(n)-space O(1) approximation algorithm for ultrametrics and prove that no single-pass exact algorithm exists, even with exponential time. - Next, we show that the algorithm for 𝓁₀ implies an O(Δ/δ) approximation for the 𝓁₁ objective, where Δ is the maximum, and δ is the minimum absolute difference between distances in the input. This bound matches the best-known approximation for the RAM model using a combinatorial algorithm when Δ/δ = O(n). - For the 𝓁_∞ objective, we provide a complete characterization of the ultrametric fitting problem. First, we present a single-pass polynomial-time Õ(n)-space 2-approximation algorithm and show that no better than 2-approximation is possible, even with exponential time. Furthermore, we show that with an additional pass, it is possible to achieve a polynomial-time exact algorithm for ultrametrics. - Finally, we extend all these results to tree metrics by using only one additional pass through the stream and without asymptotically increasing the approximation factor.
Cite as

Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis. Fitting Tree Metrics and Ultrametrics in Data Streams. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmel_et_al:LIPIcs.ICALP.2025.42,
  author =	{Carmel, Amir and Das, Debarati and Kipouridis, Evangelos and Pipis, Evangelos},
  title =	{{Fitting Tree Metrics and Ultrametrics in Data Streams}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{42:1--42:21},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-234197},
  doi =		{10.4230/LIPIcs.ICALP.2025.42},
  annote =	{Keywords: Streaming, Clustering, Ultrametrics, Tree metrics, Distance fitting}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.40
Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering

Authors: Nairen Cao, Shi Li, and Jia Ye

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

Abstract
We revisit the simultaneous approximation model for the correlation clustering problem introduced by Davies, Moseley, and Newman [Davies et al., 2024]. The objective is to find a clustering that minimizes given norms of the disagreement vector over all vertices. We present an efficient algorithm that produces a clustering that is simultaneously a 63.3-approximation for all monotone symmetric norms. This significantly improves upon the previous approximation ratio of 6348 due to Davies, Moseley, and Newman [Davies et al., 2024], which works only for 𝓁_p-norms. To achieve this result, we first reduce the problem to approximating all top-k norms simultaneously, using the connection between monotone symmetric norms and top-k norms established by Chakrabarty and Swamy [Chakrabarty and Swamy, 2019]. Then we develop a novel procedure that constructs a 12.66-approximate fractional clustering for all top-k norms. Our 63.3-approximation ratio is obtained by combining this with the 5-approximate rounding algorithm by Kalhan, Makarychev, and Zhou [Kalhan et al., 2019]. We then demonstrate that with a loss of ε in the approximation ratio, the algorithm can be adapted to run in nearly linear time and in the MPC (massively parallel computation) model with poly-logarithmic number of rounds. By allowing a further trade-off in the approximation ratio to (359+ε), the number of MPC rounds can be reduced to a constant.
Cite as

Nairen Cao, Shi Li, and Jia Ye. Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cao_et_al:LIPIcs.ICALP.2025.40,
  author =	{Cao, Nairen and Li, Shi and Ye, Jia},
  title =	{{Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{40:1--40:20},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-234171},
  doi =		{10.4230/LIPIcs.ICALP.2025.40},
  annote =	{Keywords: Correlation Clustering, All-Norms, Approximation Algorithm, Massively Parallel Algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.32
A Faster Algorithm for Constrained Correlation Clustering

Authors: Nick Fischer, Evangelos Kipouridis, Jonas Klausen, and Mikkel Thorup

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

Abstract
In the Correlation Clustering problem we are given n nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing the minimum number of violated preferences. In certain cases, however, the preference between some pairs may be too important to be violated. The constrained version of this problem specifies pairs of nodes that must be in the same cluster as well as pairs that must not be in the same cluster (hard constraints). The output clustering has to satisfy all hard constraints while minimizing the number of violated preferences. Constrained Correlation Clustering is APX-Hard and has been approximated within a factor 3 by van Zuylen et al. [SODA '07]. Their algorithm is based on rounding an LP with Θ(n³) constraints, resulting in an Ω(n^{3ω}) running time. In this work, using a more combinatorial approach, we show how to approximate this problem significantly faster at the cost of a slightly weaker approximation factor. In particular, our algorithm runs in Õ(n³) time (notice that the input size is Θ(n²)) and approximates Constrained Correlation Clustering within a factor 16. To achieve our result we need properties guaranteed by a particular influential algorithm for (unconstrained) Correlation Clustering, the CC-PIVOT algorithm. This algorithm chooses a pivot node u, creates a cluster containing u and all its preferred nodes, and recursively solves the rest of the problem. It is known that selecting pivots at random gives a 3-approximation. As a byproduct of our work, we provide a derandomization of the CC-PIVOT algorithm that still achieves the 3-approximation; furthermore, we show that there exist instances where no ordering of the pivots can give a (3-ε)-approximation, for any constant ε. Finally, we introduce a node-weighted version of Correlation Clustering, which can be approximated within factor 3 using our insights on Constrained Correlation Clustering. As the general weighted version of Correlation Clustering would require a major breakthrough to approximate within a factor o(log n), Node-Weighted Correlation Clustering may be a practical alternative.
Cite as

Nick Fischer, Evangelos Kipouridis, Jonas Klausen, and Mikkel Thorup. A Faster Algorithm for Constrained Correlation Clustering. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.STACS.2025.32,
  author =	{Fischer, Nick and Kipouridis, Evangelos and Klausen, Jonas and Thorup, Mikkel},
  title =	{{A Faster Algorithm for Constrained Correlation Clustering}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{32:1--32:18},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-228585},
  doi =		{10.4230/LIPIcs.STACS.2025.32},
  annote =	{Keywords: Clustering, Constrained Correlation Clustering, Approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.51
Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures

Authors: Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang

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

Abstract
We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the (p,q)-Steiner-Connectivity Preservation problem where we protect a minimum-cost set of edges such that the underlying graph maintains p-edge-connectivity between given terminal pairs against edge failures, assuming at most q unprotected edges can fail. We design polynomial-time exact algorithms for the cases where p and q are small and approximation algorithms for general values of p and q. Additionally, we show that when both p and q are part of the input, even deciding whether a given solution is feasible is NP-complete. This hardness also carries over to Flexible Network Design, a research direction that has gained significant attention. In particular, previous work focuses on problem settings where either p or q is constant, for which our new hardness result now provides justification.
Cite as

Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang. Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hommelsheim_et_al:LIPIcs.STACS.2025.51,
  author =	{Hommelsheim, Felix and Liu, Zhenwei and Megow, Nicole and Zhang, Guochuan},
  title =	{{Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{51:1--51:21},
  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.2025.51},
  URN =		{urn:nbn:de:0030-drops-228761},
  doi =		{10.4230/LIPIcs.STACS.2025.51},
  annote =	{Keywords: Network Design, Edge Failures, Graph Connectivity, Approximation Algorithms}
}
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