14 Search Results for "Cao, Nairen"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.48
Static to Dynamic Correlation Clustering

Authors: Nairen Cao, Vincent Cohen-Addad, Euiwoong Lee, Shi Li, David Rasmussen Lolck, Alantha Newman, Mikkel Thorup, Lukas Vogl, Shuyi Yan, and Hanwen Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [Mach. Learn. '04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimize the number of edges between vertices in different clusters and missing edges between vertices inside the same cluster. This problem has a wide application in data mining and machine learning. We introduce a general framework that transforms existing static correlation clustering algorithms into fully-dynamic ones that work against an adaptive adversary. We show how to apply our framework to known efficient correlation clustering algorithms, starting from the classic 3-approximate Pivot algorithm from Ailon, Charikar and Newman [JACM'08]. Applied to the most recent sublinear 1.485-approximation algorithm from Cao, Cohen-Addad, Lee, Li, Lolck, Newman, Thorup, Vogl, Yan and Zhang [STOC'25] , we get an 1.485-approximation fully-dynamic algorithm that works with worst-case constant update time. The original static algorithm gets its approximation factor with constant probability, and we get the same against an adaptive adversary in the sense that for any given update step, not known to our algorithm, our solution is an 1.485-approximation with constant probability when we reach this update. Most of previous dynamic algorithms, including the celebrated result from Behnezhad, Charikar, Ma and Tan [FOCS'19], had approximation factors around 3 in expectation, and they could only handle an oblivious adversary. A recent algorithm by Braverman, Dharangutte, Pai, Shah, and Wang [AISTATS'25] handles an adaptive adversary, but it has a large unspecified constant approximation ratio. This contrasts with our general transformation, which works with all the best approximation factors known for the static case.
Cite as

Nairen Cao, Vincent Cohen-Addad, Euiwoong Lee, Shi Li, David Rasmussen Lolck, Alantha Newman, Mikkel Thorup, Lukas Vogl, Shuyi Yan, and Hanwen Zhang. Static to Dynamic Correlation Clustering. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 48:1-48:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cao_et_al:LIPIcs.ICALP.2026.48,
  author =	{Cao, Nairen and Cohen-Addad, Vincent and Lee, Euiwoong and Li, Shi and Lolck, David Rasmussen and Newman, Alantha and Thorup, Mikkel and Vogl, Lukas and Yan, Shuyi and Zhang, Hanwen},
  title =	{{Static to Dynamic Correlation Clustering}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{48:1--48:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.48},
  URN =		{urn:nbn:de:0030-drops-264378},
  doi =		{10.4230/LIPIcs.ICALP.2026.48},
  annote =	{Keywords: Dynamic Algorithms, Correlation Clustering, Approximation 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.ISAAC.2025.37
Parallel Joinable B-Trees in the Fork-Join I/O Model

Authors: Michael T. Goodrich, Yan Gu, Ryuto Kitagawa, and Yihan Sun

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied. This framework has received particular attention in the parallel setting, and has been shown to be effective in enabling simple and theoretically efficient set operations on trees. Despite the widespread adoption of parallel join-based trees, a major drawback of previous work on such data structures is the inefficiency of their input/output (I/O) access patterns. Some recent work (e.g., C-trees and PaC-trees) focused on more I/O-friendly implementations of these algorithms. Surprisingly, however, there have been no results on bounding the I/O-costs for these algorithms. It remains open whether these algorithms can provide tight, provable guarantees in I/O-costs on trees. This paper studies efficient parallel algorithms for set operations based on search tree algorithms using a join-based framework, with a special focus on achieving I/O efficiency in these algorithms. To better capture the I/O-efficiency in these algorithms in parallel, we introduce a new computational model, the Fork-Join I/O Model, to measure the I/O costs in fork-join parallelism. This model measures the total block transfers (I/O work) and their critical path (I/O span). Under this model, we propose our new solution based on B-trees. Our parallel algorithm computes the union, intersection, and difference of two B-trees with O(m log_B(n/m)) I/O work and O(log_B m ⋅ log₂ log_B n + log_B n) I/O span, where n and m ≤ n are the sizes of the two trees, and B is the block size.
Cite as

Michael T. Goodrich, Yan Gu, Ryuto Kitagawa, and Yihan Sun. Parallel Joinable B-Trees in the Fork-Join I/O Model. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goodrich_et_al:LIPIcs.ISAAC.2025.37,
  author =	{Goodrich, Michael T. and Gu, Yan and Kitagawa, Ryuto and Sun, Yihan},
  title =	{{Parallel Joinable B-Trees in the Fork-Join I/O Model}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{37:1--37:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.37},
  URN =		{urn:nbn:de:0030-drops-249451},
  doi =		{10.4230/LIPIcs.ISAAC.2025.37},
  annote =	{Keywords: Parallel algorithm, I/O efficiency, search trees, B-trees}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.74
Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications

Authors: Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka

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

Abstract
Min-plus matrix multiplication is a fundamental tool for designing algorithms operating on distances in graphs and different problems solvable by dynamic programming. We know that, assuming the APSP hypothesis, no subcubic-time algorithm exists for the case of general matrices. However, in many applications the matrices admit certain structural properties that can be used to design faster algorithms. For example, when considering a planar graph, one often works with a Monge matrix A, meaning that the density matrix A^◻ has non-negative entries, that is, A^◻_{i,j} := A_{i+1,j} + A_{i,j+1} - A_{i,j} -A_{i+1,j+1} ≥ 0. The min-plus product of two n×n Monge matrices can be computed in 𝒪(n²) time using the famous SMAWK algorithm. In applications such as longest common subsequence, edit distance, and longest increasing subsequence, the matrices are even more structured, as observed by Tiskin [J. Discrete Algorithms, 2008]: they are (or can be converted to) simple unit-Monge matrices, meaning that the density matrix is a permutation matrix and, furthermore, the first column and the last row of the matrix consist of only zeroes. Such matrices admit an implicit representation of size 𝒪(n) and, as shown by Tiskin [SODA 2010 & Algorithmica, 2015], their min-plus product can be computed in 𝒪(nlog n) time. Russo [SPIRE 2010 & Theor. Comput. Sci., 2012] identified a general structural property of matrices that admit such efficient representation and min-plus multiplication algorithms: the core size δ, defined as the number of non-zero entries in the density matrices of the input and output matrices. He provided an adaptive implementation of the SMAWK algorithm that runs in 𝒪((n+δ)log³ n) or 𝒪((n+δ)log² n) time (depending on the representation of the input matrices). In this work, we further investigate the core size as the parameter that enables efficient min-plus matrix multiplication. On the combinatorial side, we provide a (linear) bound on the core size of the product matrix in terms of the core sizes of the input matrices. On the algorithmic side, we generalize Tiskin’s algorithm (but, arguably, with a more elementary analysis) to solve the core-sparse Monge matrix multiplication problem in 𝒪(n+δlog δ) ⊆ 𝒪(n + δ log n) time, matching the complexity for simple unit-Monge matrices. As witnessed by the recent work of Gorbachev and Kociumaka [STOC'25] for edit distance with integer weights, our generalization opens up the possibility of speed-ups for weighted sequence alignment problems. Furthermore, our multiplication algorithm is also capable of producing an efficient data structure for recovering the witness for any given entry of the output matrix. This allows us, for example, to preprocess an integer array of size n in Õ(n) time so that the longest increasing subsequence of any sub-array can be reconstructed in Õ(𝓁) time, where 𝓁 is the length of the reported subsequence. In comparison, Karthik C. S. and Rahul [arXiv, 2024] recently achieved 𝒪(𝓁+n^{1/2}polylog n)-time reporting after 𝒪(n^{3/2}polylog n)-time preprocessing.
Cite as

Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka. Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.74,
  author =	{Gawrychowski, Pawe{\l} and Gorbachev, Egor and Kociumaka, Tomasz},
  title =	{{Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{74:1--74:17},
  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.2025.74},
  URN =		{urn:nbn:de:0030-drops-245427},
  doi =		{10.4230/LIPIcs.ESA.2025.74},
  annote =	{Keywords: Min-plus matrix multiplication, Monge matrix, longest increasing subsequence}
}
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
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
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

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

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

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

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@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.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.ITCS.2025.13
Low Sensitivity Hopsets

Authors: Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng, Jie Gao, and Nicole Wein

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Given a weighted graph G = (V,E,w), a (β, ε)-hopset H is an edge set such that for any s,t ∈ V, where s can reach t in G, there is a path from s to t in G ∪ H which uses at most β hops whose length is in the range [dist_G(s,t), (1+ε)dist_G(s,t)]. We break away from the traditional question that asks for a hopset H that achieves small |H| and small diameter β and instead study the sensitivity of H, a new quality measure. The sensitivity of a vertex (or edge) given a hopset H is, informally, the number of times a single hop in G ∪ H bypasses it; a bit more formally, assuming shortest paths in G are unique, it is the number of hopset edges (s,t) ∈ H such that the vertex (or edge) is contained in the unique st-path in G having length exactly dist_G(s,t). The sensitivity associated with H is then the maximum sensitivity over all vertices (or edges). The highlights of our results are: - A construction for (Õ(√n), 0)-hopsets on undirected graphs with O(log n) sensitivity, complemented with a lower bound showing that Õ(√n) is tight up to polylogarithmic factors for any construction with polylogarithmic sensitivity. - A construction for (n^o(1), ε)-hopsets on undirected graphs with n^o(1) sensitivity for any ε > 0 that is at least inverse polylogarithmic, complemented with a lower bound on the tradeoff between β, ε, and the sensitivity. - We define a notion of sensitivity for β-shortcut sets (which are the reachability analogues of hopsets) and give a construction for Õ(√n)-shortcut sets on directed graphs with O(log n) sensitivity, complemented with a lower bound showing that β = Ω̃(n^{1/3}) for any construction with polylogarithmic sensitivity. We believe hopset sensitivity is a natural measure in and of itself, and could potentially find use in a diverse range of contexts. More concretely, the notion of hopset sensitivity is also directly motivated by the Differentially Private All Sets Range Queries problem [Deng et al. WADS 23]. Our result for O(log n) sensitivity (Õ(√n), 0)-hopsets on undirected graphs immediately improves the current best-known upper bound on utility from Õ(n^{1/3}) to Õ(n^{1/4}) in the pure-DP setting, which is tight up to polylogarithmic factors.
Cite as

Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng, Jie Gao, and Nicole Wein. Low Sensitivity Hopsets. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ashvinkumar_et_al:LIPIcs.ITCS.2025.13,
  author =	{Ashvinkumar, Vikrant and Bernstein, Aaron and Deng, Chengyuan and Gao, Jie and Wein, Nicole},
  title =	{{Low Sensitivity Hopsets}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-226418},
  doi =		{10.4230/LIPIcs.ITCS.2025.13},
  annote =	{Keywords: Hopsets, Shortcuts, Sensitivity, Differential Privacy}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2024.1
Recent Progress on Correlation Clustering: From Local Algorithms to Better Approximation Algorithms and Back (Invited Talk)

Authors: Vincent Cohen-Addad

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Correlation clustering is a classic model for clustering problems arising in machine learning and data mining. Given a set of data elements represented as vertices of a graph and pairwise similarity represented as edges, the goal is to find a partition of the vertex set so as to minimize the total number of edges across the parts plus the total number of non-edges within the parts. Introduced in the early 2000s [Bansal et al., 2004], correlation clustering has received a large amount of attention through the years. A natural linear programming relaxation was shown to have an integrality gap of at least 2 and at most 2.5 [Ailon et al., 2008] in 2005, and in 2015 at most 2.06 [Chawla et al., 2015]. In 2021, motivated by large-scale application new structural insights allowed to derive a simple, practical algorithm that achieved an O(1)-approximation in a variety of models (Massively Parallel, Sublinear, Streaming or Differentially-private) [Vincent Cohen{-}Addad et al., 2021; Cohen-Addad et al., 2022]. These new insights turned out to be a key building block in designing better algorithms: It serves as a pre-clustering of the input graph that enables algorithm with approximation guarantees significantly better than 2 [Vincent Cohen{-}Addad et al., 2023; Vincent Cohen{-}Addad et al., 2022]. It is a key component in the new algorithm that achieves a 1.44-approximation [Nairen Cao et al., 2024] and in the new local-search based 1.84-approximation for the Massively Parallel, Sublinear, and Streaming models [Vincent Cohen{-}Addad et al., 2024]. This talk will review the above recent development and what are the main open research directions. A collection of joint works with Nairen Cao, Silvio Lattanzi, Euiwoong Lee, Shi Li, David Rasmussen Lolck, Slobodan Mitrovic, Alantha Newman, Ashkan Norouzi-Fard, Nikos Parotsidis, Marcin Pilipczuk, Jakub Tarnawski, Mikkel Thorup, Lukas Vogl, Shuyi Yan, Hanwen Zhang.
Cite as

Vincent Cohen-Addad. Recent Progress on Correlation Clustering: From Local Algorithms to Better Approximation Algorithms and Back (Invited Talk). In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cohenaddad:LIPIcs.ESA.2024.1,
  author =	{Cohen-Addad, Vincent},
  title =	{{Recent Progress on Correlation Clustering: From Local Algorithms to Better Approximation Algorithms and Back}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.1},
  URN =		{urn:nbn:de:0030-drops-210728},
  doi =		{10.4230/LIPIcs.ESA.2024.1},
  annote =	{Keywords: Approximation Algorithms, Clustering, Local Model}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.13
Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights

Authors: Vikrant Ashvinkumar, Aaron Bernstein, Nairen Cao, Christoph Grunau, Bernhard Haeupler, Yonggang Jiang, Danupon Nanongkai, and Hsin-Hao Su

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
This paper presents parallel, distributed, and quantum algorithms for single-source shortest paths when edges can have negative integer weights (negative-weight SSSP). We show a framework that reduces negative-weight SSSP in all these settings to n^{o(1)} calls to any SSSP algorithm that works on inputs with non-negative integer edge weights (non-negative-weight SSSP) with a virtual source. More specifically, for a directed graph with m edges, n vertices, undirected hop-diameter D, and polynomially bounded integer edge weights, we show randomized algorithms for negative-weight SSSP with - W_{SSSP}(m,n)n^{o(1)} work and S_{SSSP}(m,n)n^{o(1)} span, given access to a non-negative-weight SSSP algorithm with W_{SSSP}(m,n) work and S_{SSSP}(m,n) span in the parallel model, and - T_{SSSP}(n,D)n^{o(1)} rounds, given access to a non-negative-weight SSSP algorithm that takes T_{SSSP}(n,D) rounds in CONGEST, and - Q_{SSSP}(m,n)n^{o(1)} quantum edge queries, given access to a non-negative-weight SSSP algorithm that takes Q_{SSSP}(m,n) queries in the quantum edge query model. This work builds off the recent result of Bernstein, Nanongkai, Wulff-Nilsen [Bernstein et al., 2022], which gives a near-linear time algorithm for negative-weight SSSP in the sequential setting. Using current state-of-the-art non-negative-weight SSSP algorithms yields randomized algorithms for negative-weight SSSP with - m^{1+o(1)} work and n^{1/2+o(1)} span in the parallel model, and - (n^{2/5}D^{2/5} + √n + D)n^{o(1)} rounds in CONGEST, and - m^{1/2}n^{1/2+o(1)} quantum queries to the adjacency list or n^{1.5+o(1)} quantum queries to the adjacency matrix. Up to a n^{o(1)} factor, the parallel and distributed results match the current best upper bounds for reachability [Jambulapati et al., 2019; Cao et al., 2021]. Consequently, any improvement to negative-weight SSSP in these models beyond the n^{o(1)} factor necessitates an improvement to the current best bounds for reachability. The quantum result matches the lower bound up to an n^{o(1)} factor [Aija Berzina et al., 2004]. Our main technical contribution is an efficient reduction from computing a low-diameter decomposition (LDD) of directed graphs to computations of non-negative-weight SSSP with a virtual source. Efficiently computing an LDD has heretofore only been known for undirected graphs in both the parallel and distributed models, and been rather unstudied in quantum models. The directed LDD is a crucial step of the sequential algorithm in [Bernstein et al., 2022], and we think that its applications to other problems in parallel and distributed models are far from being exhausted. Other ingredients of our results include altering the recursion structure of the scaling algorithm in [Bernstein et al., 2022] to surmount difficulties that arise in these models, and also an efficient reduction from computing strongly connected components to computations of SSSP with a virtual source in CONGEST. The latter result answers a question posed in [Bernstein and Nanongkai, 2019] in the negative.
Cite as

Vikrant Ashvinkumar, Aaron Bernstein, Nairen Cao, Christoph Grunau, Bernhard Haeupler, Yonggang Jiang, Danupon Nanongkai, and Hsin-Hao Su. Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ashvinkumar_et_al:LIPIcs.ESA.2024.13,
  author =	{Ashvinkumar, Vikrant and Bernstein, Aaron and Cao, Nairen and Grunau, Christoph and Haeupler, Bernhard and Jiang, Yonggang and Nanongkai, Danupon and Su, Hsin-Hao},
  title =	{{Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.13},
  URN =		{urn:nbn:de:0030-drops-210849},
  doi =		{10.4230/LIPIcs.ESA.2024.13},
  annote =	{Keywords: Parallel algorithm, distributed algorithm, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.36
Nested Active-Time Scheduling

Authors: Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to g jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. In this way, the active time models parallel scheduling when there is a fixed cost for turning the machine on at each discrete step. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This result improves on the previous best 2-approximation for the general case.
Cite as

Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh. Nested Active-Time Scheduling. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2022.36,
  author =	{Cao, Nairen and Fineman, Jeremy T. and Li, Shi and Mestre, Juli\'{a}n and Russell, Katina and Umboh, Seeun William},
  title =	{{Nested Active-Time Scheduling}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.36},
  URN =		{urn:nbn:de:0030-drops-173214},
  doi =		{10.4230/LIPIcs.ISAAC.2022.36},
  annote =	{Keywords: Scheduling algorithms, Active time, Approximation algorithm}
}
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