15 Search Results for "Allen-Zhu, Zeyuan"

Document
DOI: 10.4230/LIPIcs.STACS.2026.6
Threshold-Driven Streaming Graph: Expansion and Rumor Spreading

Authors: Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
A randomized distributed algorithm called RAES was introduced in [Becchetti et al., 2020] to extract a bounded-degree expander from a dense n-vertex expander graph G = (V, E). The algorithm relies on a simple threshold-based procedure. A key assumption in [Becchetti et al., 2020] is that the input graph G is static - i.e., both its vertex set V and edge set E remain unchanged throughout the process - while the analysis of raes in dynamic models is left as a major open question. In this work, we investigate the behavior of RAES under a dynamic graph model induced by a streaming node-churn process (also known as the sliding window model), where, at each discrete round, a new node joins the graph and the oldest node departs. This process yields a bounded-degree dynamic graph 𝒢 = {G_t = (V_t, E_t) : t ∈ ℕ} that captures essential characteristics of peer-to-peer networks - specifically, node churn and threshold on the number of connections each node can manage. We prove that every snapshot G_t in the dynamic graph sequence has good expansion properties with high probability. Furthermore, we leverage this property to establish a logarithmic upper bound on the completion time of the well-known PUSH and PULL rumor spreading protocols over the dynamic graph 𝒢.
Cite as

Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi. Threshold-Driven Streaming Graph: Expansion and Rumor Spreading. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{angileri_et_al:LIPIcs.STACS.2026.6,
  author =	{Angileri, Flora and Clementi, Andrea and Natale, Emanuele and Salvi, Michele and Ziccardi, Isabella},
  title =	{{Threshold-Driven Streaming Graph: Expansion and Rumor Spreading}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.6},
  URN =		{urn:nbn:de:0030-drops-254957},
  doi =		{10.4230/LIPIcs.STACS.2026.6},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Dynamic Random Graphs, Graph Expansion, Rumor Spreading}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.38
Fully Dynamic Spectral Sparsification for Directed Hypergraphs

Authors: Sebastian Forster, Gramoz Goranci, and Ali Momeni

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph sparsifiers of directed hypergraphs. Our algorithm achieves a near-optimal size of O(n² / ε ² log ⁷ m) and amortized update time of O(r² log ³ m), where n is the number of vertices, and m and r respectively upper bound the number of hyperedges and the rank of the hypergraph at any time. We also extend our approach to the parallel batch-dynamic setting, where a batch of any k hyperedge insertions or deletions can be processed with O(kr² log ³ m) amortized work and O(log ² m) depth. This constitutes the first spectral-based sparsification algorithm in this setting.
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Sebastian Forster, Gramoz Goranci, and Ali Momeni. Fully Dynamic Spectral Sparsification for Directed Hypergraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{forster_et_al:LIPIcs.STACS.2026.38,
  author =	{Forster, Sebastian and Goranci, Gramoz and Momeni, Ali},
  title =	{{Fully Dynamic Spectral Sparsification for Directed Hypergraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{38:1--38:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.38},
  URN =		{urn:nbn:de:0030-drops-255272},
  doi =		{10.4230/LIPIcs.STACS.2026.38},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.69
Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time

Authors: Etienne Objois and Adrian Vladu

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We provide the first nearly-linear time algorithm for approximating 𝓁_{q → p}-norms of non-negative matrices, for q ≥ p ≥ 1. Our algorithm returns a (1-ε)-approximation to the matrix norm in time Õ(1/(q ε) ⋅ nnz(A)), where A is the input matrix, and improves upon the previous state of the art, which either proved convergence only in the limit [Boyd '74], or had very high polynomial running times [Bhaskara-Vijayraghavan, SODA '11]. Our algorithm is extremely simple, and is largely inspired from the coordinate-scaling approach used for positive linear program solvers. Our algorithm can readily be used in the [Englert-Räcke, FOCS '09] to improve the running time of constructing O(log n)-competitive 𝓁_p-oblivious routings.
Cite as

Etienne Objois and Adrian Vladu. Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 69:1-69:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{objois_et_al:LIPIcs.STACS.2026.69,
  author =	{Objois, Etienne and Vladu, Adrian},
  title =	{{Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{69:1--69:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.69},
  URN =		{urn:nbn:de:0030-drops-255585},
  doi =		{10.4230/LIPIcs.STACS.2026.69},
  annote =	{Keywords: matrix norm, Perron-Frobenius theory, oblivious routings, input-sparsity time, lp norm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.32
Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem

Authors: Jin-Yi Cai and Ben Young

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

Abstract
Valiant’s Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets ℱ and 𝒢 of tensors (a.k.a. constraint functions or signatures) are related by a holographic transformation, then ℱ and 𝒢 are Holant-indistinguishable, i.e., every tensor network using tensors from ℱ, respectively from 𝒢, contracts to the same value. Xia (ICALP 2010) conjectured the converse of the Holant theorem, but a counterexample was found based on vanishing signatures, those which are Holant-indistinguishable from 0. We prove two near-converses of the Holant theorem using techniques from invariant theory. (I) Holant-indistinguishable ℱ and 𝒢 always admit two sequences of holographic transformations mapping them arbitrarily close to each other, i.e., their GL_q-orbit closures intersect. (II) We show that vanishing signatures are the only true obstacle to a converse of the Holant theorem. As corollaries of the two theorems we obtain the first characterization of homomorphism-indistinguishability over graphs of bounded degree, a long standing open problem, and show that two graphs with invertible adjacency matrices are isomorphic if and only if they are homomorphism-indistinguishable over graphs with maximum degree at most three. We also show that Holant-indistinguishability is complete for a complexity class TOCI introduced by Lysikov and Walter [Vladimir Lysikov and Michael Walter, 2024], and hence hard for graph isomorphism.
Cite as

Jin-Yi Cai and Ben Young. Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cai_et_al:LIPIcs.ITCS.2026.32,
  author =	{Cai, Jin-Yi and Young, Ben},
  title =	{{Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{32:1--32:20},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-253198},
  doi =		{10.4230/LIPIcs.ITCS.2026.32},
  annote =	{Keywords: Holant, Orbit Closure Intersection, Homomorphism Indistinguishability, Tensor Network}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.1
Rule-Based Knowledge Graph Completion (Invited Paper)

Authors: Patrick Betz, Christian Meilicke, and Heiner Stuckenschmidt

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
The field of knowledge graph completion is concerned with augmenting knowledge graphs with missing information. Symbolic rule-based approaches are not only efficient and interpretable but also competitive with embedding-based methods in regard to predictive quality. Rule-based knowledge graph completion can be separated into two stages, the learning stage and the application stage, which are both individually challenging. In the learning stage, horn rules are mined from a given knowledge graph. Given the vast size of the space of all possible rules, the mining approach must select relevant rules effectively. In the application stage, the mined rules are used to make new predictions which are assigned with plausibility scores. These scores need to be set by aggregating individual confidence values of rules that have the same consequence. This tutorial covers the fundamental aspects required to build a symbolic rule-based approach for knowledge graph completion. It will discuss the different rule types, mining strategies, and how to effectively apply the rules in different scenarios. Finally, we discuss practical examples for rule application by using the Python-based PyClause library.
Cite as

Patrick Betz, Christian Meilicke, and Heiner Stuckenschmidt. Rule-Based Knowledge Graph Completion (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 1:1-1:45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{betz_et_al:OASIcs.RW.2024/2025.1,
  author =	{Betz, Patrick and Meilicke, Christian and Stuckenschmidt, Heiner},
  title =	{{Rule-Based Knowledge Graph Completion}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{1:1--1:45},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.1},
  URN =		{urn:nbn:de:0030-drops-250461},
  doi =		{10.4230/OASIcs.RW.2024/2025.1},
  annote =	{Keywords: Knowledge Graph Completion, Rule Learning, Symbolic AI}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.70
Improved Parallel Derandomization via Finite Automata with Applications

Authors: Jeff Giliberti and David G. Harris

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

Abstract
A central approach to algorithmic derandomization is the construction of small-support probability distributions that "fool” randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling polynomial-space statistical tests computed via finite automata [Sivakumar STOC'02]; this encompasses a wide range of properties including k-wise independence and sums of random variables. We present new parallel algorithms to fool finite-state automata, with significantly reduced processor complexity. Briefly, our approach is to iteratively sparsify distributions using a work-efficient lattice rounding routine and maintain accuracy by tracking an aggregate weighted error that is determined by the Lipschitz value of the statistical tests being fooled. We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding. These involve further several optimizations, such as the truncation of the state space of the automata and FFT-based convolutions to compute transition probabilities efficiently.
Cite as

Jeff Giliberti and David G. Harris. Improved Parallel Derandomization via Finite Automata with Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{giliberti_et_al:LIPIcs.ESA.2025.70,
  author =	{Giliberti, Jeff and Harris, David G.},
  title =	{{Improved Parallel Derandomization via Finite Automata with Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{70:1--70:17},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-245381},
  doi =		{10.4230/LIPIcs.ESA.2025.70},
  annote =	{Keywords: Parallel Algorithms, Derandomization, MAX-CUT, Gale-Berlekamp Switching Game}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.6
Decremental (1+ε)-Approximate Maximum Eigenvector: Dynamic Power Method

Authors: Deeksha Adil and Thatchaphol Saranurak

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

Abstract
We present a dynamic algorithm for maintaining (1+ε)-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix A undergoing decreasing updates, i.e., updates which may only decrease eigenvalues. Given a vector v updating A ← A-vv^⊤, our algorithm takes Õ(nnz(v)) amortized update time, i.e., polylogarithmic per non-zeros in the update vector. Our technique is based on a novel analysis of the influential power method in the dynamic setting. The two previous sets of techniques have the following drawbacks (1) algebraic techniques can maintain exact solutions but their update time is at least polynomial per non-zeros, and (2) sketching techniques admit polylogarithmic update time but suffer from a crude additive approximation. Our algorithm exploits an oblivious adversary. Interestingly, we show that any algorithm with polylogarithmic update time per non-zeros that works against an adaptive adversary and satisfies an additional natural property would imply a breakthrough for checking psd-ness of matrices in Õ(n²) time, instead of O(n^ω) time.
Cite as

Deeksha Adil and Thatchaphol Saranurak. Decremental (1+ε)-Approximate Maximum Eigenvector: Dynamic Power Method. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adil_et_al:LIPIcs.ICALP.2025.6,
  author =	{Adil, Deeksha and Saranurak, Thatchaphol},
  title =	{{Decremental (1+\epsilon)-Approximate Maximum Eigenvector: Dynamic Power Method}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.6},
  URN =		{urn:nbn:de:0030-drops-233834},
  doi =		{10.4230/LIPIcs.ICALP.2025.6},
  annote =	{Keywords: Power Method, Dynamic 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.2025.29
Extracting Dual Solutions via Primal Optimizers

Authors: Yair Carmon, Arun Jambulapati, Liam O'Carroll, and Aaron Sidford

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

Abstract
We provide a general method to convert a "primal" black-box algorithm for solving regularized convex-concave minimax optimization problems into an algorithm for solving the associated dual maximin optimization problem. Our method adds recursive regularization over a logarithmic number of rounds where each round consists of an approximate regularized primal optimization followed by the computation of a dual best response. We apply this result to obtain new state-of-the-art runtimes for solving matrix games in specific parameter regimes, obtain improved query complexity for solving the dual of the CVaR distributionally robust optimization (DRO) problem, and recover the optimal query complexity for finding a stationary point of a convex function.
Cite as

Yair Carmon, Arun Jambulapati, Liam O'Carroll, and Aaron Sidford. Extracting Dual Solutions via Primal Optimizers. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 29:1-29:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmon_et_al:LIPIcs.ITCS.2025.29,
  author =	{Carmon, Yair and Jambulapati, Arun and O'Carroll, Liam and Sidford, Aaron},
  title =	{{Extracting Dual Solutions via Primal Optimizers}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{29:1--29:24},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-226578},
  doi =		{10.4230/LIPIcs.ITCS.2025.29},
  annote =	{Keywords: Minimax optimization, black-box optimization, matrix games, distributionally robust optimization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.47
Concentration of Submodular Functions and Read-k Families Under Negative Dependence

Authors: Sharmila Duppala, George Z. Li, Juan Luque, Aravind Srinivasan, and Renata Valieva

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

Abstract
We study the question of whether submodular functions of random variables satisfying various notions of negative dependence satisfy Chernoff-like concentration inequalities. We prove such a concentration inequality for the lower tail when the random variables satisfy negative association or negative regression, partially resolving an open problem raised in ([Frederick Qiu and Sahil Singla, 2022]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms ([Chandra Chekuri et al., 2010; Nicholas J. A. Harvey and Neil Olver, 2014]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read-k families [Dmitry Gavinsky et al., 2015] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [Dmitry Gavinsky et al., 2015].
Cite as

Sharmila Duppala, George Z. Li, Juan Luque, Aravind Srinivasan, and Renata Valieva. Concentration of Submodular Functions and Read-k Families Under Negative Dependence. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{duppala_et_al:LIPIcs.ITCS.2025.47,
  author =	{Duppala, Sharmila and Li, George Z. and Luque, Juan and Srinivasan, Aravind and Valieva, Renata},
  title =	{{Concentration of Submodular Functions and Read-k Families Under Negative Dependence}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{47:1--47:16},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-226751},
  doi =		{10.4230/LIPIcs.ITCS.2025.47},
  annote =	{Keywords: Chernoff bounds, Submodular Functions, Negative Correlation}
}
Document
Position
DOI: 10.4230/TGDK.1.1.2
Large Language Models and Knowledge Graphs: Opportunities and Challenges

Authors: Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Large Language Models (LLMs) have taken Knowledge Representation - and the world - by storm. This inflection point marks a shift from explicit knowledge representation to a renewed focus on the hybrid representation of both explicit knowledge and parametric knowledge. In this position paper, we will discuss some of the common debate points within the community on LLMs (parametric knowledge) and Knowledge Graphs (explicit knowledge) and speculate on opportunities and visions that the renewed focus brings, as well as related research topics and challenges.
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Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux. Large Language Models and Knowledge Graphs: Opportunities and Challenges. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 2:1-2:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{pan_et_al:TGDK.1.1.2,
  author =	{Pan, Jeff Z. and Razniewski, Simon and Kalo, Jan-Christoph and Singhania, Sneha and Chen, Jiaoyan and Dietze, Stefan and Jabeen, Hajira and Omeliyanenko, Janna and Zhang, Wen and Lissandrini, Matteo and Biswas, Russa and de Melo, Gerard and Bonifati, Angela and Vakaj, Edlira and Dragoni, Mauro and Graux, Damien},
  title =	{{Large Language Models and Knowledge Graphs: Opportunities and Challenges}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:38},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.2},
  URN =		{urn:nbn:de:0030-drops-194766},
  doi =		{10.4230/TGDK.1.1.2},
  annote =	{Keywords: Large Language Models, Pre-trained Language Models, Knowledge Graphs, Ontology, Retrieval Augmented Language Models}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.62
Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration

Authors: Michael B. Cohen, Aaron Sidford, and Kevin Tian

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We show that standard extragradient methods (i.e. mirror prox [Arkadi Nemirovski, 2004] and dual extrapolation [Yurii Nesterov, 2007]) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide fine-grained characterization of the convergence rates of extragradient methods for solving monotone variational inequalities in terms of a natural condition we call relative Lipschitzness. We further generalize this framework to handle local and randomized notions of relative Lipschitzness and thereby recover rates for box-constrained 𝓁_∞ regression based on area convexity [Jonah Sherman, 2017] and complexity bounds achieved by accelerated (randomized) coordinate descent [Zeyuan {Allen Zhu} et al., 2016; Yurii Nesterov and Sebastian U. Stich, 2017] for smooth convex function minimization.
Cite as

Michael B. Cohen, Aaron Sidford, and Kevin Tian. Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 62:1-62:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2021.62,
  author =	{Cohen, Michael B. and Sidford, Aaron and Tian, Kevin},
  title =	{{Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{62:1--62:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.62},
  URN =		{urn:nbn:de:0030-drops-136011},
  doi =		{10.4230/LIPIcs.ITCS.2021.62},
  annote =	{Keywords: Variational inequalities, minimax optimization, acceleration, 𝓁\underline∞ regression}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.3
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent

Authors: Zeyuan Allen-Zhu and Lorenzo Orecchia

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. We observe that the performances of gradient and mirror descent are complementary, so that faster algorithms can be designed by "linearly coupling" the two. We show how to reconstruct Nesterov's accelerated gradient methods using linear coupling, which gives a cleaner interpretation than Nesterov's original proofs. We also discuss the power of linear coupling by extending it to many other settings that Nesterov's methods cannot apply to.
Cite as

Zeyuan Allen-Zhu and Lorenzo Orecchia. Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{allenzhu_et_al:LIPIcs.ITCS.2017.3,
  author =	{Allen-Zhu, Zeyuan and Orecchia, Lorenzo},
  title =	{{Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.3},
  URN =		{urn:nbn:de:0030-drops-81850},
  doi =		{10.4230/LIPIcs.ITCS.2017.3},
  annote =	{Keywords: linear coupling, gradient descent, mirror descent, acceleration}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.53
Optimization Algorithms for Faster Computational Geometry

Authors: Zeyuan Allen-Zhu, Zhenyu Liao, and Yang Yuan

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by m hyperplanes, and the minimum enclosing ball (MinEB) of a set of n points, both in d-dimensional space. We improve the running time of iterative algorithms on MaxIB from ~O(m*d*alpha^3/epsilon^3) to ~O(m*d + m*sqrt(d)*alpha/epsilon), a speed-up up to ~O(sqrt(d)*alpha^2/epsilon^2), and MinEB from ~O(n*d/sqrt(epsilon)) to ~O(n*d + n*sqrt(d)/sqrt(epsilon)), a speed-up up to ~O(sqrt(d)). Our improvements are based on a novel saddle-point optimization framework. We propose a new algorithm L1L2SPSolver for solving a class of regularized saddle-point problems, and apply a randomized Hadamard space rotation which is a technique borrowed from compressive sensing. Interestingly, the motivation of using Hadamard rotation solely comes from our optimization view but not the original geometry problem: indeed, it is not immediately clear why MaxIB or MinEB, as a geometric problem, should be easier to solve if we rotate the space by a unitary matrix. We hope that our optimization perspective sheds lights on solving other geometric problems as well.
Cite as

Zeyuan Allen-Zhu, Zhenyu Liao, and Yang Yuan. Optimization Algorithms for Faster Computational Geometry. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 53:1-53:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{allenzhu_et_al:LIPIcs.ICALP.2016.53,
  author =	{Allen-Zhu, Zeyuan and Liao, Zhenyu and Yuan, Yang},
  title =	{{Optimization Algorithms for Faster Computational Geometry}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{53:1--53:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.53},
  URN =		{urn:nbn:de:0030-drops-63325},
  doi =		{10.4230/LIPIcs.ICALP.2016.53},
  annote =	{Keywords: maximum inscribed balls, minimum enclosing balls, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.451
Restricted Isometry Property for General p-Norms

Authors: Zeyuan Allen-Zhu, Rati Gelashvili, and Ilya Razenshteyn

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an m x n matrix satisfies RIP of order k for the L_p norm, if |Ax|_p is approximately |x|_p for every x with at most k non-zero coordinates. For every 1 <= p < infty we obtain almost tight bounds on the minimum number of rows m necessary for the RIP property to hold. Prior to this work, only the cases p = 1, 1 + 1/log(k), and 2 were studied. Interestingly, our results show that the case p=2 is a "singularity" point: the optimal number of rows m is Theta(k^p) for all p in [1, infty)-{2}, as opposed to Theta(k) for k=2. We also obtain almost tight bounds for the column sparsity of RIP matrices and discuss implications of our results for the Stable Sparse Recovery problem.
Cite as

Zeyuan Allen-Zhu, Rati Gelashvili, and Ilya Razenshteyn. Restricted Isometry Property for General p-Norms. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 451-460, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{allenzhu_et_al:LIPIcs.SOCG.2015.451,
  author =	{Allen-Zhu, Zeyuan and Gelashvili, Rati and Razenshteyn, Ilya},
  title =	{{Restricted Isometry Property for General p-Norms}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{451--460},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.451},
  URN =		{urn:nbn:de:0030-drops-51273},
  doi =		{10.4230/LIPIcs.SOCG.2015.451},
  annote =	{Keywords: compressive sensing, dimension reduction, linear algebra, high-dimensional geometry}
}
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