30 Search Results for "Schramm, Tselil"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.85
Recovering Communities in Structured Random Graphs

Authors: Michael Kapralov, Luca Trevisan, and Weronika Wrzos-Kaminska

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

Abstract
The problem of recovering planted community structure in random graphs has received a lot of attention in the literature on the stochastic block model, where the input is a random graph in which edges crossing between different communities appear with smaller probability than edges induced by communities. The communities themselves form a collection of vertex-disjoint sparse cuts in the expected graph, and can be recovered, often exactly, from a sample as long as a separation condition on the intra- and inter-community edge probabilities is satisfied. In this paper, we ask whether the presence of a large number of overlapping sparsest cuts in the expected graph still allows recovery. For example, the d-dimensional hypercube graph admits d distinct (balanced) sparsest cuts, one for every coordinate. Can these cuts be identified given a random sample of the edges of the hypercube where each edge is present independently with some probability p ∈ (0, 1)? We show that this is the case, in a very strong sense: the sparsest balanced cut in a sample of the hypercube at rate p = Clog d/d for a sufficiently large constant C is 1/poly(d)-close to a coordinate cut with high probability. This is asymptotically optimal and allows approximate recovery of all d cuts simultaneously. Furthermore, for an appropriate sample of hypercube-like graphs recovery can be made exact. The proof is essentially a strong hypercube cut sparsification bound that combines a theorem of Friedgut, Kalai and Naor on boolean functions whose Fourier transform concentrates on the first level of the Fourier spectrum with Karger’s cut counting argument.
Cite as

Michael Kapralov, Luca Trevisan, and Weronika Wrzos-Kaminska. Recovering Communities in Structured Random Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 85:1-85:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kapralov_et_al:LIPIcs.ITCS.2026.85,
  author =	{Kapralov, Michael and Trevisan, Luca and Wrzos-Kaminska, Weronika},
  title =	{{Recovering Communities in Structured Random Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{85:1--85:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.85},
  URN =		{urn:nbn:de:0030-drops-253727},
  doi =		{10.4230/LIPIcs.ITCS.2026.85},
  annote =	{Keywords: Hypercube graphs, Community detection, Fourier analysis of Boolean functions}
}
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.ESA.2025.100
Cut-Query Algorithms with Few Rounds

Authors: Yotam Kenneth-Mordoch and Robert Krauthgamer

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

Abstract
In the cut-query model, the algorithm can access the input graph G = (V,E) only via cut queries that report, given a set S ⊆ V, the total weight of edges crossing the cut between S and V⧵ S. This model was introduced by Rubinstein, Schramm and Weinberg [ITCS'18] and its investigation has so far focused on the number of queries needed to solve optimization problems, such as global minimum cut. We turn attention to the round complexity of cut-query algorithms, and show that several classical problems can be solved in this model with only a constant number of rounds. Our main results are algorithms for finding a minimum cut in a graph, that offer different tradeoffs between round complexity and query complexity, where n = |V| and δ(G) denotes the minimum degree of G: (i) Õ(n^{4/3}) cut queries in two rounds in unweighted graphs; (ii) Õ(rn^{1+1/r}/δ(G)^{1/r}) queries in 2r+1 rounds for any integer r ≥ 1 again in unweighted graphs; and (iii) Õ(rn^{1+(1+log_n W)/r}) queries in 4r+3 rounds for any r ≥ 1 in weighted graphs. We also provide algorithms that find a minimum (s,t)-cut and approximate the maximum cut in a few rounds.
Cite as

Yotam Kenneth-Mordoch and Robert Krauthgamer. Cut-Query Algorithms with Few Rounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 100:1-100:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kennethmordoch_et_al:LIPIcs.ESA.2025.100,
  author =	{Kenneth-Mordoch, Yotam and Krauthgamer, Robert},
  title =	{{Cut-Query Algorithms with Few Rounds}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{100:1--100:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.100},
  URN =		{urn:nbn:de:0030-drops-245692},
  doi =		{10.4230/LIPIcs.ESA.2025.100},
  annote =	{Keywords: Cut Queries, Round Complexity, Submodular Optimization}
}
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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.30
Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs

Authors: Zhangsong Li

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

Abstract
In this paper, assuming a natural strengthening of the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erdős-Rényi graphs G(n,q;ρ) when the edge-density q = n^{-1+o(1)} and the correlation ρ < √{α} lies below the Otter’s threshold, this resolves a remaining problem in [Jian Ding et al., 2023]; (2) the detection problem between a pair of correlated sparse stochastic block model S(n,λ/n;k,ε;s) and a pair of independent stochastic block models S(n,λs/n;k,ε) when ε² λ s < 1 lies below the Kesten-Stigum (KS) threshold and s < √α lies below the Otter’s threshold, this resolves a remaining problem in [Guanyi Chen et al., 2024]. One of the main ingredient in our proof is to derive certain forms of algorithmic contiguity between two probability measures based on bounds on their low-degree advantage. To be more precise, consider the high-dimensional hypothesis testing problem between two probability measures ℙ and ℚ based on the sample Y. We show that if the low-degree advantage Adv_{≤D}(dℙ/dℚ) = O(1), then (assuming the low-degree conjecture) there is no efficient algorithm A such that ℚ(A(Y) = 0) = 1-o(1) and ℙ(A(Y) = 1) = Ω(1). This framework provides a useful tool for performing reductions between different inference tasks.
Cite as

Zhangsong Li. Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li:LIPIcs.APPROX/RANDOM.2025.30,
  author =	{Li, Zhangsong},
  title =	{{Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{30:1--30:18},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-243965},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.30},
  annote =	{Keywords: Algorithmic Contiguity, Low-degree Conjecture, Correlated Random Graphs}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.48
Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT

Authors: Eren C. Kızıldağ

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

Abstract
The Ising p-spin glass and random k-SAT are two canonical examples of disordered systems that play a central role in understanding the link between geometric features of optimization landscapes and computational tractability. Both models exhibit hard regimes where all known polynomial-time algorithms fail and possess the multi Overlap Gap Property (m-OGP), an intricate geometrical property that rigorously rules out a broad class of algorithms exhibiting input stability. We establish that, in both models, the symmetric m-OGP undergoes a sharp phase transition, and we pinpoint its exact threshold. For the Ising p-spin glass, our results hold for all sufficiently large p; for the random k-SAT, they apply to all k growing mildly with the number of Boolean variables. Notably, our findings yield qualitative insights into the power of OGP-based arguments. A particular consequence for the Ising p-spin glass is that the strength of the m-OGP in establishing algorithmic hardness grows without bound as m increases. These are the first sharp threshold results for the m-OGP. Our analysis hinges on a judicious application of the second moment method, enhanced by concentration. While a direct second moment calculation fails, we overcome this via a refined approach that leverages an argument of Frieze [Frieze, 1990] and exploiting concentration properties of carefully constructed random variables.
Cite as

Eren C. Kızıldağ. Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kizildag:LIPIcs.APPROX/RANDOM.2025.48,
  author =	{K{\i}z{\i}lda\u{g}, Eren C.},
  title =	{{Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{48:1--48:16},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-244147},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.48},
  annote =	{Keywords: spin glasses, p-spin model, random constraint satisfaction problems, overlap gap property, phase transitions, computational complexity}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.5
Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT

Authors: Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma

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

Abstract
This paper studies complete k-Constraint Satisfaction Problems (CSPs), where an n-variable instance has exactly one nontrivial constraint for each subset of k variables, i.e., it has binom(n,k) constraints. A recent work started a systematic study of complete k-CSPs [Anand, Lee, Sharma, SODA'25], and showed a quasi-polynomial time algorithm that decides if there is an assignment satisfying all the constraints of any complete Boolean-alphabet k-CSP, algorithmically separating complete instances from dense instances. The tractability of this decision problem is necessary for any nontrivial (multiplicative) approximation for the minimization version, whose goal is to minimize the number of violated constraints. The same paper raised the question of whether it is possible to obtain nontrivial approximation algorithms for complete Min-k-CSPs with k ≥ 3. In this work, we make progress in this direction and show a quasi-polynomial time polylog(n)-approximation to Min-NAE-3-SAT on complete instances, which asks to minimize the number of 3-clauses where all the three literals equal the same bit. To the best of our knowledge, this is the first known example of a CSP whose decision version is NP-Hard in general (and dense) instances while admitting a polylog(n)-approximation in complete instances. Our algorithm presents a new iterative framework for rounding a solution from the Sherali-Adams hierarchy, where each iteration interleaves the two well-known rounding tools: the conditioning procedure, in order to "almost fix" many variables, and the thresholding procedure, in order to "completely fix" them. Finally, we improve the running time of the decision algorithms of Anand, Lee, and Sharma and show a simple algorithm that decides any complete Boolean-alphabet k-CSP in polynomial time.
Cite as

Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma. Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2025.5,
  author =	{Anand, Aditya and Lee, Euiwoong and Mazzali, Davide and Sharma, Amatya},
  title =	{{Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{5:1--5:23},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-243712},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  annote =	{Keywords: Constraint Satisfiability Problems, Approximation Algorithms, Sherali Adams}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.16
Sparsest Cut and Eigenvalue Multiplicities on Low Degree Abelian Cayley Graphs

Authors: Tommaso d'Orsi, Chris Jones, Jake Ruotolo, Salil Vadhan, and Jiyu Zhang

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

Abstract
Whether or not the Sparsest Cut problem admits an efficient O(1)-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut, we present a novel, simple algorithm that combines eigenspace enumeration with a new algorithm for the Cut Improvement problem. The runtime of our algorithm is parametrized by a quantity that we call the solution dimension SD_ε(G): the smallest k such that the subspace spanned by the first k Laplacian eigenvectors contains all but ε fraction of a sparsest cut. Our algorithm matches the guarantees of prior methods based on the threshold-rank paradigm, while also extending beyond them. To illustrate this, we study its performance on low degree Cayley graphs over Abelian groups - canonical examples of graphs with poor expansion properties. We prove that low degree Abelian Cayley graphs have small solution dimension, yielding an algorithm that computes a (1+ε)-approximation to the uniform Sparsest Cut of a degree-d Cayley graph over an Abelian group of size n in time n^O(1) ⋅ exp{(d/ε)^O(d)}. Along the way to bounding the solution dimension of Abelian Cayley graphs, we analyze their sparse cuts and spectra, proving that the collection of O(1)-approximate sparsest cuts has an ε-net of size exp{(d/ε)^O(d)} and that the multiplicity of λ₂ is bounded by 2^O(d). The latter bound is tight and improves on a previous bound of 2^O(d²) by Lee and Makarychev.
Cite as

Tommaso d'Orsi, Chris Jones, Jake Ruotolo, Salil Vadhan, and Jiyu Zhang. Sparsest Cut and Eigenvalue Multiplicities on Low Degree Abelian Cayley Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dorsi_et_al:LIPIcs.APPROX/RANDOM.2025.16,
  author =	{d'Orsi, Tommaso and Jones, Chris and Ruotolo, Jake and Vadhan, Salil and Zhang, Jiyu},
  title =	{{Sparsest Cut and Eigenvalue Multiplicities on Low Degree Abelian Cayley Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{16:1--16:20},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-243827},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.16},
  annote =	{Keywords: Sparsest Cut, Spectral Graph Theory, Cayley Graphs, Approximation Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.17
Spectral Refutations of Semirandom k-LIN over Larger Fields

Authors: Nicholas Kocurek and Peter Manohar

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

Abstract
We study the problem of strongly refuting semirandom k-LIN(𝔽) instances: systems of k-sparse inhomogeneous linear equations over a finite field 𝔽. For the case of 𝔽 = 𝔽₂, this is the well-studied problem of refuting semirandom instances of k-XOR, where the works of [Venkatesan Guruswami et al., 2022; Jun-Ting Hsieh et al., 2023] establish a tight trade-off between runtime and clause density for refutation: for any choice of a parameter 𝓁, they give an n^{O(𝓁)}-time algorithm to certify that there is no assignment that can satisfy more than 1/2 + ε-fraction of constraints in a semirandom k-XOR instance, provided that the instance has O(n)⋅(n/𝓁)^{k/2 - 1} log n/ε⁴ constraints, and the work of [Pravesh K. Kothari et al., 2017] provides good evidence that this tight up to a polylog(n) factor via lower bounds for the Sum-of-Squares hierarchy. However, for larger fields, the only known results for this problem are established via black-box reductions to the case of 𝔽₂, resulting in a |𝔽|^{3k} gap between the current best upper and lower bounds. In this paper, we give an algorithm for refuting semirandom k-LIN(𝔽) instances with the "correct" dependence on the field size |𝔽|. For any choice of a parameter 𝓁, our algorithm runs in (|𝔽|)^O(𝓁)-time and strongly refutes semirandom k-LIN(𝔽) instances with at least O(n) ⋅ (|𝔽^*| n/𝓁) ^{k/2 - 1} log(n|𝔽^*|)/ε⁴ constraints. We give good evidence that this dependence on the field size |𝔽| is optimal by proving a lower bound for the Sum-of-Squares hierarchy that matches this threshold up to a polylog(n |𝔽^*|) factor. Our results also extend beyond finite fields to the more general case of ℤ_m and arbitrary finite Abelian groups. Our key technical innovation is a generalization of the "𝔽₂ Kikuchi matrices" of [Alexander S. Wein et al., 2019; Venkatesan Guruswami et al., 2022] to larger fields, and finite Abelian groups more generally.
Cite as

Nicholas Kocurek and Peter Manohar. Spectral Refutations of Semirandom k-LIN over Larger Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kocurek_et_al:LIPIcs.APPROX/RANDOM.2025.17,
  author =	{Kocurek, Nicholas and Manohar, Peter},
  title =	{{Spectral Refutations of Semirandom k-LIN over Larger Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{17:1--17:15},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-243834},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.17},
  annote =	{Keywords: Spectral Algorithms, CSP Refutation, Kikuchi Matrices}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.32
A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion

Authors: Anastasia Sofronova and Dmitry Sokolov

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

Abstract
Random Δ-CNF formulas are one of the few candidates that are expected to be hard for proof systems and SAT algotirhms. Assume we sample m clauses over n variables. Here, the main complexity parameter is clause density, χ := m/n. For a fixed Δ, there exists a satisfiability threshold c_Δ such that for χ > c_Δ a formula is unsatisfiable with high probability. and for χ < c_Δ it is satisfiable with high probability. Near satisfiability threshold, there are various lower bounds for algorithms and proof systems [Eli Ben-Sasson, 2001; Eli Ben-Sasson and Russell Impagliazzo, 1999; Michael Alekhnovich and Alexander A. Razborov, 2003; Dima Grigoriev, 2001; Grant Schoenebeck, 2008; Pavel Hrubes and Pavel Pudlák, 2017; Noah Fleming et al., 2017; Dmitry Sokolov, 2024], and for high-density regimes, there exist upper bounds [Uriel Feige et al., 2006; Sebastian Müller and Iddo Tzameret, 2014; Jackson Abascal et al., 2021; Venkatesan Guruswami et al., 2022]. One of the frontiers in the direction of proving lower bounds on these formulas is the k-DNF Resolution proof system (aka Res(k)). There are several known results for k = 𝒪(√{log n}/{log log n}}) [Nathan Segerlind et al., 2004; Michael Alekhnovich, 2011], that are applicable only for density regime near the threshold. In this paper, we show the first Res(k) lower bound that is applicable in higher-density regimes. Our results work for slightly larger k = 𝒪(√{log n}).
Cite as

Anastasia Sofronova and Dmitry Sokolov. A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 32:1-32:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sofronova_et_al:LIPIcs.CCC.2025.32,
  author =	{Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{32:1--32:27},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-237269},
  doi =		{10.4230/LIPIcs.CCC.2025.32},
  annote =	{Keywords: proof complexity, random CNFs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.7
Sparser Abelian High Dimensional Expanders

Authors: Yotam Dikstein, Siqi Liu, and Avi Wigderson

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

Abstract
The focus of this paper is the development of new elementary techniques for the construction and analysis of high dimensional expanders. Specifically, we present two new explicit constructions of Cayley high dimensional expanders (HDXs) over the abelian group 𝔽₂ⁿ. Our expansion proofs use only linear algebra and combinatorial arguments. The first construction gives local spectral HDXs of any constant dimension and subpolynomial degree exp(n^ε) for every ε > 0, improving on a construction by Golowich [Golowich, 2023] which achieves ε = 1/2. [Golowich, 2023] derives these HDXs by sparsifying the complete Grassmann poset of subspaces. The novelty in our construction is the ability to sparsify any expanding Grassmann posets, leading to iterated sparsification and much smaller degrees. The sparse Grassmannian (which is of independent interest in the theory of HDXs) serves as the generating set of the Cayley graph. Our second construction gives a 2-dimensional HDX of any polynomial degree exp(ε n) for any constant ε > 0, which is simultaneously a spectral expander and a coboundary expander. To the best of our knowledge, this is the first such non-trivial construction. We name it the Johnson complex, as it is derived from the classical Johnson scheme, whose vertices serve as the generating set of this Cayley graph. This construction may be viewed as a derandomization of the recent random geometric complexes of [Liu et al., 2023]. Establishing coboundary expansion through Gromov’s "cone method" and the associated isoperimetric inequalities is the most intricate aspect of this construction. While these two constructions are quite different, we show that they both share a common structure, resembling the intersection patterns of vectors in the Hadamard code. We propose a general framework of such "Hadamard-like" constructions in the hope that it will yield new HDXs.
Cite as

Yotam Dikstein, Siqi Liu, and Avi Wigderson. Sparser Abelian High Dimensional Expanders. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 7:1-7:98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dikstein_et_al:LIPIcs.CCC.2025.7,
  author =	{Dikstein, Yotam and Liu, Siqi and Wigderson, Avi},
  title =	{{Sparser Abelian High Dimensional Expanders}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{7:1--7:98},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-237013},
  doi =		{10.4230/LIPIcs.CCC.2025.7},
  annote =	{Keywords: Local spectral expander, coboundary expander, Grassmannian expander}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.11
Switching Graph Matrix Norm Bounds: From i.i.d. to Random Regular Graphs

Authors: Jeff Xu

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

Abstract
In this work, we give novel spectral norm bounds for graph matrix on inputs being random regular graphs. Graph matrix is a family of random matrices with entries given by polynomial functions of the underlying input. These matrices have been known to be the backbone for the analysis of various average-case algorithms and hardness. Previous investigations of such matrices are largely restricted to the Erdős-Rényi model, and tight matrix norm bounds on regular graphs are only known for specific examples. We unite these two lines of investigations, and give the first result departing from the Erdős-Rényi setting in the full generality of graph matrices. We believe our norm bound result would enable a simple transfer of spectral analysis for average-case algorithms and hardness between these two distributions of random graphs. As an application of our spectral norm bounds, we show that higher-degree Sum-of-Squares lower bounds for the independent set problem on Erdős-Rényi random graphs can be switched into lower bounds on random d-regular graphs. Our main conceptual insight is that existing Sum-of-Squares lower bounds analysis based on moment methods are surprisingly robust, and amenable for a light-weight translation. Our result is the first to address the general open question of analyzing higher-degree Sum-of-Squares on random regular graphs.
Cite as

Jeff Xu. Switching Graph Matrix Norm Bounds: From i.i.d. to Random Regular Graphs. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{xu:LIPIcs.CCC.2025.11,
  author =	{Xu, Jeff},
  title =	{{Switching Graph Matrix Norm Bounds: From i.i.d. to Random Regular Graphs}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{11:1--11:23},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-237054},
  doi =		{10.4230/LIPIcs.CCC.2025.11},
  annote =	{Keywords: Semidefinite programming, random matrices, average-case complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.28
Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition

Authors: Vishwas Bhargava and Devansh Shringi

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

Abstract
We present a deterministic 2^{k^{𝒪(1)}} poly(n,d) time algorithm for decomposing d-dimensional, width-n tensors of rank at most k over ℝ and ℂ. This improves upon the previous randomized algorithm of Peleg, Shpilka, and Volk (ITCS '24) that takes 2^{k^{k^{𝒪(k)}}} poly(n,d) time and the deterministic n^k^k time algorithms of Bhargava, Saraf, and Volkovich (STOC '21). Our work resolves an open question asked by Peleg, Shpilka, and Volk (ITCS '24) on whether a deterministic Fixed Parameter Tractable (FPT) algorithm exists for worst-case tensor decomposition. We also make substantial progress on the fundamental problem of how the tractability of tensor decomposition varies as the tensor rank increases. Our result implies that we can achieve deterministic polynomial-time decomposition as long as the rank of the tensor is at most (log n)^{1/C}, where C is some fixed constant independent of n and d. Further, we note that there cannot exist a polynomial-time algorithm for k = ω(log n) unless ETH fails. Our algorithm works for all fields; however, the time complexity worsens to 2^{k^{k^{𝒪(1)}}} and requires randomization for finite fields of large characteristics. Both conditions are provably necessary unless there are improvements in the state of the art for system solving over the corresponding fields. Our approach achieves this by designing a proper learning (reconstruction) algorithm for set-multilinear depth-3 arithmetic circuits. On a technical note, we design a "partial" clustering algorithm for set-multilinear depth-3 arithmetic circuits that lets us isolate a cluster from any set-multilinear depth-3 circuit while preserving the structure of the circuit.
Cite as

Vishwas Bhargava and Devansh Shringi. Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhargava_et_al:LIPIcs.ICALP.2025.28,
  author =	{Bhargava, Vishwas and Shringi, Devansh},
  title =	{{Faster \& Deterministic FPT Algorithm for Worst-Case Tensor Decomposition}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{28:1--28:20},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-234052},
  doi =		{10.4230/LIPIcs.ICALP.2025.28},
  annote =	{Keywords: Algebraic circuits, Deterministic algorithms, FPT algorithm, Learning circuits, Reconstruction, Tensor Decomposition, Tensor Rank}
}
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}
}
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