93 Search Results for "Ene, Alina"

Volume

LIPIcs, Volume 353

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

APPROX/RANDOM 2025, August 11-13, 2025, Berkeley, CA, USA

Editors: Alina Ene and Eshan Chattopadhyay

Document
DOI: 10.4230/LIPIcs.STACS.2026.16
To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs

Authors: Sander Borst and Moritz Venzin

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

Abstract
We study the rent-or-buy variant of the online Steiner forest problem on node- and edge-weighted graphs. For n-node graphs with at most ̄{n} nodes of non-zero weight, and at most k̃ different arriving terminal pairs, we obtain the following: - A deterministic, O(log n log ̄{n})-competitive algorithm against adaptive adversaries. This improves on the previous best, O(log⁴ n)-competitive algorithm obtained by the black-box reduction from [Yair Bartal et al., 2001] combined with the previously best deterministic algorithms for the simpler "buy-only" setting. - A deterministic, O(̄{n}log k̃)-competitive algorithm against adaptive adversaries. This generalizes the O(log k̃)-competitive algorithm for the purely edge-weighted setting from [Seeun Umboh, 2015]. - A randomized, O(log k̃ log ̄{n})-competitive algorithm against oblivious adversaries. All previous approaches were based on the randomized, black-box reduction from [Awerbuch et al., 2004] that achieves a O(log k̃ log n)-competitive ratio when combined with an algorithm for the "buy-only" setting. Our key technical ingredient is a novel charging scheme to an instance of online prize-collecting set cover. This allows us to extend the witness-technique of [Seeun Umboh, 2015] to the node-weighted setting and obtain refined guarantees with respect to ̄{n}, already in the much simpler "buy-only" setting.
Cite as

Sander Borst and Moritz Venzin. To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{borst_et_al:LIPIcs.STACS.2026.16,
  author =	{Borst, Sander and Venzin, Moritz},
  title =	{{To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{16:1--16:16},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-255054},
  doi =		{10.4230/LIPIcs.STACS.2026.16},
  annote =	{Keywords: online network design, node-weighted Steiner forest, derandomization}
}
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.2026.105
Fixed-Parameter Tractable Submodular Maximization over a Matroid

Authors: Shamisa Nematollahi, Adrian Vladu, and Junyao Zhao

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

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

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

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@InProceedings{nematollahi_et_al:LIPIcs.ITCS.2026.105,
  author =	{Nematollahi, Shamisa and Vladu, Adrian and Zhao, Junyao},
  title =	{{Fixed-Parameter Tractable Submodular Maximization over a Matroid}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{105:1--105:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.105},
  URN =		{urn:nbn:de:0030-drops-253924},
  doi =		{10.4230/LIPIcs.ITCS.2026.105},
  annote =	{Keywords: Submodular maximization, matroids, parameterized complexity, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.3
Parameterized Maximum Node-Disjoint Paths

Authors: Michael Lampis and Manolis Vasilakis

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We revisit the Maximum Node-Disjoint Paths problem, the natural optimization version of the famous Node-Disjoint Paths problem, where we are given an undirected graph G, k (demand) pairs of vertices (s_i, t_i), and an integer 𝓁, and are asked whether there exist at least 𝓁 vertex-disjoint paths in G whose endpoints are given pairs. This problem has been intensely studied from both the approximation and parameterized complexity point of view and is notably known to be intractable by standard structural parameters, such as tree-depth, as well as the combined parameter 𝓁 plus pathwidth. We present several results improving and clarifying this state of the art, with an emphasis towards FPT approximation. Our main positive contribution is to show that the problem’s intractability can be overcome using approximation: We show that for several of the structural parameters for which the problem is hard, most notably tree-depth, the problem admits an efficient FPT approximation scheme, returning a (1-ε)-approximate solution in time f(td,ε)n^𝒪(1). We manage to obtain these results by comprehensively mapping out the structural parameters for which the problem is FPT if 𝓁 is also a parameter, hence showing that understanding 𝓁 as a parameter is key to the problem’s approximability. This, in turn, is a problem we are able to solve via a surprisingly simple color-coding algorithm, which relies on identifying an insightful problem-specific variant of the natural parameter, namely the number of vertices used in the solution. The results above are quite encouraging, as they indicate that in some situations where the problem does not admit an FPT algorithm, it is still solvable almost to optimality in FPT time. A natural question is whether the FPT approximation algorithm we devised for tree-depth can be extended to pathwidth. We resolve this negatively, showing that under the Parameterized Inapproximability Hypothesis no FPT approximation scheme for this parameter is possible, even in time f(pw,ε)n^g(ε). We thus precisely determine the parameter border where the problem transitions from "hard but approximable" to "inapproximable". Lastly, we strengthen existing lower bounds by replacing W[1]-hardness by XNLP-completeness for parameter pathwidth, and improving the n^o(√{td}) ETH-based lower bound for tree-depth to (the optimal) n^o(td).
Cite as

Michael Lampis and Manolis Vasilakis. Parameterized Maximum Node-Disjoint Paths. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lampis_et_al:LIPIcs.IPEC.2025.3,
  author =	{Lampis, Michael and Vasilakis, Manolis},
  title =	{{Parameterized Maximum Node-Disjoint Paths}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.3},
  URN =		{urn:nbn:de:0030-drops-251357},
  doi =		{10.4230/LIPIcs.IPEC.2025.3},
  annote =	{Keywords: ETH, Maximum Node-Disjoint Paths, Parameterized Complexity, PIH}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.10
A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design

Authors: Caleb Eardley, Dalton Gomez, Ryan Dupuis, Michael Papadopoulos, and Sean Yaw

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
The Multi-Capacity Fixed-Charge Network Flow (MC-FCNF) problem, a generalization of the Fixed-Charge Network Flow problem, aims to assign capacities to edges in a flow network such that a target amount of flow can be hosted at minimum cost. The cost model for both problems dictates that the fixed cost of an edge is incurred for any non-zero amount of flow hosted by that edge. This problem naturally arises in many areas including infrastructure design, transportation, telecommunications, and supply chain management. The MC-FCNF problem is NP-Hard, so solving large instances using exact techniques is impractical. This paper presents a genetic algorithm designed to quickly find high-quality flow solutions to the MC-FCNF problem. The genetic algorithm uses a novel solution representation scheme that eliminates the need to repair invalid flow solutions, which is an issue common to many other genetic algorithms for the MC-FCNF problem. The genetic algorithm’s utility is demonstrated with an evaluation using real-world CO₂ capture, transportation, and storage infrastructure design data. The evaluation results highlight the genetic algorithm’s potential for solving large-scale network design problems.
Cite as

Caleb Eardley, Dalton Gomez, Ryan Dupuis, Michael Papadopoulos, and Sean Yaw. A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eardley_et_al:OASIcs.ATMOS.2025.10,
  author =	{Eardley, Caleb and Gomez, Dalton and Dupuis, Ryan and Papadopoulos, Michael and Yaw, Sean},
  title =	{{A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{10:1--10:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.10},
  URN =		{urn:nbn:de:0030-drops-247661},
  doi =		{10.4230/OASIcs.ATMOS.2025.10},
  annote =	{Keywords: Fixed-Charge Network Flow, Genetic Algorithm, Matheuristic, Infrastructure Design}
}
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.2025.107
Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts

Authors: Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang

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

Abstract
We show the existence of length-constrained expander decomposition in directed graphs and undirected vertex-capacitated graphs. Previously, its existence was shown only in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2022; Haeupler et al., 2024]. Along the way, we prove the multi-commodity maxflow-mincut theorems for length-constrained expansion in both directed and undirected vertex-capacitated graphs. Based on our decomposition, we build a length-constrained flow shortcut for undirected vertex-capacitated graphs, which roughly speaking is a set of edges and vertices added to the graph so that every multi-commodity flow demand can be routed with approximately the same vertex-congestion and length, but all flow paths only contain few edges. This generalizes the shortcut for undirected edge-capacitated graphs from [Bernhard Haeupler et al., 2024]. Length-constrained expander decomposition and flow shortcuts have been crucial in the recent algorithms in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2024; Haeupler et al., 2024]. Our work thus serves as a foundation to generalize these concepts to directed and vertex-capacitated graphs.
Cite as

Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang. Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 107:1-107:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haeupler_et_al:LIPIcs.ESA.2025.107,
  author =	{Haeupler, Bernhard and Long, Yaowei and Saranurak, Thatchaphol and Wang, Shengzhe},
  title =	{{Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{107:1--107:17},
  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.2025.107},
  URN =		{urn:nbn:de:0030-drops-245765},
  doi =		{10.4230/LIPIcs.ESA.2025.107},
  annote =	{Keywords: Length-Constrained Expander, Expander Decomposition, Shortcut}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.31
New Statistical and Computational Results for Learning Junta Distributions

Authors: Lorenzo Beretta

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

Abstract
We study the problem of learning junta distributions on {±1}ⁿ, where a distribution is a k-junta if its probability mass function depends on a subset of at most k variables. We make two main contributions: - We show that learning k-junta distributions is computationally equivalent to learning k-parity functions with noise (LPN), a landmark problem in computational learning theory. - We design an algorithm for learning junta distributions whose statistical complexity is optimal, up to polylogarithmic factors. Computationally, our algorithm matches the complexity of previous (non-sample-optimal) algorithms. Combined, our two contributions imply that our algorithm cannot be significantly improved, statistically or computationally, barring a breakthrough for LPN.
Cite as

Lorenzo Beretta. New Statistical and Computational Results for Learning Junta Distributions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beretta:LIPIcs.APPROX/RANDOM.2025.31,
  author =	{Beretta, Lorenzo},
  title =	{{New Statistical and Computational Results for Learning Junta Distributions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{31:1--31:23},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-243978},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.31},
  annote =	{Keywords: Junta Distributions, Learning Parities with Noise}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.37
Permanental Rank vs Determinantal Rank of Random Matrices over Finite Fields

Authors: Fatemeh Ghasemi, Gal Gross, and Swastik Kopparty

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

Abstract
This paper is motivated by basic complexity and probability questions about permanents of random matrices over small finite fields, and in particular, about properties separating the permanent and the determinant. Let q be a fixed odd prime, and let k ≤ n both be growing. For a uniformly random n × k matrix A over 𝔽_q, we study the probability that all k × k submatrices of A have zero permanent; namely that A does not have full permanental rank. When k = n, this is simply the probability that a random square matrix over 𝔽_q has zero permanent, which we do not understand. We believe that the probability in this case is 1/q + o(1), which would be in contrast to the case of the determinant, where the answer is 1/q + Ω_q(1). Our main result is that when k is O(√n), the probability that a random n × k matrix does not have full permanental rank is essentially the same as the probability that the matrix has a 0 column, namely (1 +o(1)) k/qⁿ. In contrast, for determinantal (standard) rank the analogous probability is Θ(q^k/q^n). At the core of our result are some basic linear algebraic properties of the permanent that distinguish it from the determinant.
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Fatemeh Ghasemi, Gal Gross, and Swastik Kopparty. Permanental Rank vs Determinantal Rank of Random Matrices over Finite Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghasemi_et_al:LIPIcs.APPROX/RANDOM.2025.37,
  author =	{Ghasemi, Fatemeh and Gross, Gal and Kopparty, Swastik},
  title =	{{Permanental Rank vs Determinantal Rank of Random Matrices over Finite Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{37:1--37:15},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-244037},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.37},
  annote =	{Keywords: Permanent, random matrices over a finite field}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.38
Low-Degree Polynomials Are Good Extractors

Authors: Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, and João Ribeiro

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

Abstract
We prove that random low-degree polynomials (over 𝔽₂) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to our work, such results were only known for the small families of (1) uniform sources, (2) affine sources, and (3) local sources. We significantly generalize these results, and prove the following. 1) Low-degree polynomials extract from small families. We show that a random low-degree polynomial is a good low-error extractor for any small family of sources. In particular, we improve the positive result of Alrabiah, Chattopadhyay, Goodman, Li, and Ribeiro (ICALP 2022) for local sources, and give new results for polynomial and variety sources via a single unified approach. 2) Low-degree polynomials extract from sumset sources. We show that a random low-degree polynomial is a good extractor for sumset sources, which are the most general large family of sources (capturing independent sources, interleaved sources, small-space sources, and more). Formally, for any even d, we show that a random degree d polynomial is an ε-error extractor for n-bit sumset sources with min-entropy k = O(d(n/ε²)^{2/d}). This is nearly tight in the polynomial error regime. Our results on sumset extractors imply new complexity separations for linear ROBPs, and the tools that go into its proof may be of independent interest. The two main tools we use are a new structural result on sumset-punctured Reed-Muller codes, paired with a novel type of reduction between extractors. Using the new structural result, we obtain new limits on the power of sumset extractors, strengthening and generalizing the impossibility results of Chattopadhyay, Goodman, and Gurumukhani (ITCS 2024).
Cite as

Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, and João Ribeiro. Low-Degree Polynomials Are Good Extractors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 38:1-38:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alrabiah_et_al:LIPIcs.APPROX/RANDOM.2025.38,
  author =	{Alrabiah, Omar and Goodman, Jesse and Mosheiff, Jonathan and Ribeiro, Jo\~{a}o},
  title =	{{Low-Degree Polynomials Are Good Extractors}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{38:1--38:25},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-244048},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.38},
  annote =	{Keywords: randomness extractors, low-degree polynomials, local sources, polynomial sources, variety sources, sumset sources, sumset extractors, Reed-Muller codes, lower bounds}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.52
Tarski Lower Bounds from Multi-Dimensional Herringbones

Authors: Simina Brânzei, Reed C. Phillips, and Nicholas J. Recker

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

Abstract
Tarski’s theorem states that every monotone function from a complete lattice to itself has a fixed point. We analyze the query complexity of finding such a fixed point on the k-dimensional grid of side length n under the ≤ relation. In this setting, there is an unknown monotone function f: {0,1,…, n-1}^k → {0,1,…, n-1}^k and an algorithm must query a vertex v to learn f(v). The goal is to find a fixed point of f using as few oracle queries as possible. We show that the randomized query complexity of this problem is Ω((k⋅log²n)/log k) for all n,k ≥ 2. This unifies and improves upon two prior results: a lower bound of Ω(log²n) from [Etessami et al., 2020] and a lower bound of Ω((k⋅log(n)/log(k)) from [Brânzei et al., 2024], respectively.
Cite as

Simina Brânzei, Reed C. Phillips, and Nicholas J. Recker. Tarski Lower Bounds from Multi-Dimensional Herringbones. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 52:1-52:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{branzei_et_al:LIPIcs.APPROX/RANDOM.2025.52,
  author =	{Br\^{a}nzei, Simina and Phillips, Reed C. and Recker, Nicholas J.},
  title =	{{Tarski Lower Bounds from Multi-Dimensional Herringbones}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{52:1--52:12},
  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.2025.52},
  URN =		{urn:nbn:de:0030-drops-244186},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.52},
  annote =	{Keywords: Tarski’s theorem, monotone functions, lattices, fixed points, computational complexity, oracle model, query complexity, lower bounds}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.54
New Constructions of Pseudorandom Codes

Authors: Surendra Ghentiyala and Venkatesan Guruswami

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

Abstract
Introduced in [Christ and Gunn, 2024], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally indistinguishable from random for an adversary that does not have the secret key, but anyone with the secret key is able to efficiently decode corrupted codewords. In this work, we examine the assumptions under which PRCs with robustness to a constant error rate exist. 1) We show that if both the planted hyperloop assumption introduced in [Andrej Bogdanov et al., 2023] and security of a version of Goldreich’s PRG hold, then there exist public-key PRCs for which no efficient adversary can distinguish a polynomial number of codewords from random with better than o(1) advantage. 2) We revisit the construction of [Christ and Gunn, 2024] and show that it can be based on a wider range of assumptions than presented in [Christ and Gunn, 2024]. To do this, we introduce a weakened version of the planted XOR assumption which we call the weak planted XOR assumption and which may be of independent interest. 3) We initiate the study of PRCs which are secure against space-bounded adversaries. We show how to construct secret-key PRCs of length O(n) which are unconditionally indistinguishable from random by poly(n) time, O(n^{1.5-ε}) space adversaries.
Cite as

Surendra Ghentiyala and Venkatesan Guruswami. New Constructions of Pseudorandom Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 54:1-54:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghentiyala_et_al:LIPIcs.APPROX/RANDOM.2025.54,
  author =	{Ghentiyala, Surendra and Guruswami, Venkatesan},
  title =	{{New Constructions of Pseudorandom Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{54:1--54:22},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-244202},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.54},
  annote =	{Keywords: Error-correcting codes, Watermarking, Pseudorandomness}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.63
Structured-Seed Local Pseudorandom Generators and Their Applications

Authors: Benny Applebaum, Dung Bui, Geoffroy Couteau, and Nikolas Melissaris

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

Abstract
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a generic template for constructing SSL-PRGs that combines the following two ingredients: [i.] 1) noisy‑NC⁰ PRGs, computable by constant‑depth circuits fed with sparse noise, with 2) new local compression schemes for sparse vectors derived from combinatorial batch codes. Instantiating the template under the sparse Learning‑Parity‑with‑Noise (LPN) assumption yields the first SSL-PRGs with polynomial stretch and constant locality from a subquadratic‑sample search hardness assumption; a mild strengthening of sparse‑LPN gives strong SSL-PRGs of arbitrary polynomial stretch. We further show that for all standard noise distributions, noisy‑local PRGs cannot be emulated by ordinary local PRGs, thereby separating the two notions. Plugging SSL-PRGs into existing frameworks, we revisit the canonical applications of local PRGs and demonstrate that SSL-PRGs suffice for: (i) indistinguishability obfuscation, (ii) constant-overhead secure computation, (iii) compact homomorphic secret sharing, and (iv) deriving hardness results for PAC‑learning DNFs from sparse‑LPN. Our work thus broadens the landscape of low‑depth pseudorandomness and anchors several primitives to a common, well‑motivated assumption.
Cite as

Benny Applebaum, Dung Bui, Geoffroy Couteau, and Nikolas Melissaris. Structured-Seed Local Pseudorandom Generators and Their Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 63:1-63:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{applebaum_et_al:LIPIcs.APPROX/RANDOM.2025.63,
  author =	{Applebaum, Benny and Bui, Dung and Couteau, Geoffroy and Melissaris, Nikolas},
  title =	{{Structured-Seed Local Pseudorandom Generators and Their Applications}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{63:1--63:26},
  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.2025.63},
  URN =		{urn:nbn:de:0030-drops-244293},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.63},
  annote =	{Keywords: Pseudorandom Generator, Local Pseudorandom Generators, Secure Computation, Obfuscation, Hardness of Learning, Local Compression}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.40
Sublinear Space Graph Algorithms in the Continual Release Model

Authors: Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou

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

Abstract
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously known edge-differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-value estimates (not vertex subset solutions) and do not use sublinear space. Instead, they rely on computing exact graph statistics on the input [Hendrik Fichtenberger et al., 2021; Shuang Song et al., 2018]. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge-differentially private algorithms use sublinear space with respect to the number of edges in the graph while some also achieve sublinear space in the number of vertices in the graph. In addition, for the densest subgraph problem, we also output edge-differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets. We make novel use of assorted sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space, continual release setting. This includes algorithms for densest subgraph, maximum matching, as well as the first continual release k-core decomposition algorithm. We also develop a novel sparse level data structure for k-core decomposition that may be of independent interest. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.
Cite as

Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou. Sublinear Space Graph Algorithms in the Continual Release Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 40:1-40:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epasto_et_al:LIPIcs.APPROX/RANDOM.2025.40,
  author =	{Epasto, Alessandro and Liu, Quanquan C. and Mukherjee, Tamalika and Zhou, Felix},
  title =	{{Sublinear Space Graph Algorithms in the Continual Release Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{40:1--40:27},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-244064},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  annote =	{Keywords: Differential Privacy, Continual Release, Densest Subgraph, k-Core Decomposition, Maximum Matching}
}
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