28 Search Results for "Kindler, Guy"

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.CSL.2026.45
Reasoning About Quality in Hyperproperties

Authors: Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Hyperproperties allow one to specify properties of systems that inherently involve not single executions of the system, but several of them at once: observational determinism and non-inference are two examples of such properties used to study the security of systems. Logics like HyperLTL have been studied in the past to model check hyperproperties of systems. However, most of the time, requiring strict security properties is actually ineffective as systems do not meet such requirements. To overcome this issue, we introduce qualitative reasoning in HyperLTL, inspired by a similar work on LTL by Almagor, Boker and Kupferman [Almagor et al., 2016] where a formula has a value in the interval [0, 1], obtained by considering either a propositional quality (how much the specification is satisfied), or a temporal quality (when the specification is satisfied). We show decidability of the approximated model checking problem, as well as the model checking of large fragments.
Cite as

Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot. Reasoning About Quality in Hyperproperties. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{graepler_et_al:LIPIcs.CSL.2026.45,
  author =	{Graepler, Samuel and Monmege, Benjamin and Talbot, Jean-Marc},
  title =	{{Reasoning About Quality in Hyperproperties}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.45},
  URN =		{urn:nbn:de:0030-drops-254704},
  doi =		{10.4230/LIPIcs.CSL.2026.45},
  annote =	{Keywords: Hyperlogics, Automata-based model checking, Quantitative verification}
}
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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.42
On the Spectral Expansion of Monotone Subsets of the Hypercube

Authors: Yumou Fei and Renato Ferreira Pinto Jr.

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

Abstract
We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset A ⊆ {0,1}ⁿ of density μ(A), the previous best lower bound on the spectral gap, due to Cohen [Cohen, 2016], was γ ≳ μ(A)/n², improving upon the earlier bound γ ≳ μ(A)²/n² established by Ding and Mossel [Ding and Mossel, 2014]. In this paper, we prove the optimal lower bound γ ≳ μ(A)/n. As a corollary, we improve the mixing time upper bound of the random walk on constant-density monotone sets from O(n³), as shown by Ding and Mossel, to O(n²). Along the way, we develop two new inequalities that may be of independent interest: (1) a directed L²-Poincaré inequality on the hypercube, and (2) an "approximate" FKG inequality for monotone sets.
Cite as

Yumou Fei and Renato Ferreira Pinto Jr.. On the Spectral Expansion of Monotone Subsets of the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 42:1-42:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fei_et_al:LIPIcs.APPROX/RANDOM.2025.42,
  author =	{Fei, Yumou and Ferreira Pinto Jr., Renato},
  title =	{{On the Spectral Expansion of Monotone Subsets of the Hypercube}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{42:1--42:24},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-244081},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  annote =	{Keywords: Random walks, mixing time, FKG inequality, Poincar\'{e} inequality, directed isoperimetry}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.27
Triangles Improve 0.878 Approximation for Maxcut

Authors: Fredie George, Anand Louis, and Rameesh Paul

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

Abstract
Maxcut is a fundamental problem in graph algorithms, extensively studied for its theoretical and practical significance. The goal is to partition the vertex set of a graph G = (V, E) into disjoint subsets S and V⧵S so as to maximize the number of edges crossing the cut (S,V⧵S). The seminal work of Goemans and Williamson [Goemans and Williamson, 1995] introduced a semidefinite programming (SDP) based algorithm achieving a α_{GW} ≈ 0.87856-approximation for general graphs, guaranteed to be optimal under the Unique Games Conjecture [Khot, 2002; Khot et al., 2007]. We revisit the Goemans–Williamson SDP and prove that the standard Maxcut SDP achieves a (α_{GW} + Ω(1))-approximation whenever the input graph contains Ω(|E|) edge-disjoint triangles. Our analysis builds on classical rounding techniques studied in [Goemans and Williamson, 1995; Zwick, 1999] and introduces a refined understanding of the SDP solution structure in regimes where the previous guarantees are tight. Our result identifies a simple combinatorial property that may be satisfied by many natural graph classes. As applications, we show that unit ball graphs and graphs satisfying a spectral transitivity condition (as studied in [Gupta et al., 2016; Basu et al., 2024]) meet our structural criterion, and therefore we get better than α_{GW} approximation guarantees for them. Our algorithm runs in nearly linear time 𝒪̃(|E|), offering a more practical alternative to the PTAS of [Jansen et al., 2005] for unit ball graphs, which has exponential dependence on the approximation parameter.
Cite as

Fredie George, Anand Louis, and Rameesh Paul. Triangles Improve 0.878 Approximation for Maxcut. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 27:1-27:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{george_et_al:LIPIcs.APPROX/RANDOM.2025.27,
  author =	{George, Fredie and Louis, Anand and Paul, Rameesh},
  title =	{{Triangles Improve 0.878 Approximation for Maxcut}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{27:1--27:25},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-243931},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.27},
  annote =	{Keywords: Approximation Algorithms, Maxcut, Semidefinite Programming, Edge-disjoint Triangles, Unit Ball Graphs, Spectral Triadic Graphs}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.66
Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

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

Abstract
Let f and g be Boolean functions over a finite Abelian group 𝒢, where g is fully known and f is accessible via queries; that is, given any x ∈ 𝒢, we can obtain the value f(x). We study the problem of tolerant isomorphism testing: given parameters ε ≥ 0 and τ > 0, the goal is to determine, using as few queries as possible, whether there exists an automorphism σ of 𝒢 such that the fractional Hamming distance between f∘σ and g is at most ε, or whether for every automorphism σ, the distance is at least ε + τ. We design an efficient tolerant property testing algorithm for this problem over finite Abelian groups with constant exponent. The exponent of a finite group refers to the largest order of any element in the group. The query complexity of our algorithm is polynomial in s and 1/τ, where s bounds the spectral norm of the function g, and τ is the tolerance parameter. In addition, we present an improved algorithm in the case where g is Fourier sparse, meaning that its Fourier expansion contains only a small number of nonzero coefficients. Our approach draws on key ideas from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner product defined over finite Abelian groups. We believe that these techniques will be useful more broadly in the design of property testing algorithms.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Testing Isomorphism of Boolean Functions over Finite Abelian Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{datta_et_al:LIPIcs.APPROX/RANDOM.2025.66,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Testing Isomorphism of Boolean Functions over Finite Abelian Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{66:1--66:22},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-244328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  annote =	{Keywords: Analysis of Boolean functions, Abelian groups, Automorphism group, Function isomorphism, Spectral norm}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.3
Maximum And- vs. Even-SAT

Authors: Tamio-Vesa Nakajima and Stanislav Živný

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

Abstract
A multiset of literals, called a clause, is strongly satisfied by an assignment if no literal evaluates to false. Finding an assignment that maximises the number of strongly satisfied clauses is NP-hard. We present a simple algorithm that finds, given a multiset of clauses that admits an assignment that strongly satisfies ρ of the clauses, an assignment in which at least ρ of the clauses are weakly satisfied, in the sense that an even number of literals evaluate to false. In particular, this implies an efficient algorithm for finding an undirected cut of value ρ in a graph G given that a directed cut of value ρ in G is promised to exist. A similar argument also gives an efficient algorithm for finding an acyclic subgraph of G with ρ edges under the same promise.
Cite as

Tamio-Vesa Nakajima and Stanislav Živný. Maximum And- vs. Even-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 3:1-3:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nakajima_et_al:LIPIcs.APPROX/RANDOM.2025.3,
  author =	{Nakajima, Tamio-Vesa and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Maximum And- vs. Even-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{3:1--3:8},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-243696},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.3},
  annote =	{Keywords: approximation, promise constraint satisfaction, max and, max even, max cut, max dicut, max acyclic}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.5
Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT

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

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

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

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

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2025.5,
  author =	{Anand, Aditya and Lee, Euiwoong and Mazzali, Davide and Sharma, Amatya},
  title =	{{Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  URN =		{urn:nbn:de:0030-drops-243712},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  annote =	{Keywords: Constraint Satisfiability Problems, Approximation Algorithms, Sherali Adams}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.13
Max-Cut with Multiple Cardinality Constraints

Authors: Yury Makarychev, Madhusudhan Reddy Pittu, and Ali Vakilian

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

Abstract
We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph G = (V, E), a partition of the vertices into c disjoint parts V₁, …, V_c, and cardinality parameters k₁, …, k_c, the goal is to select a set S ⊆ V such that |S ∩ V_i| = k_i for each i ∈ [c], maximizing the total weight of edges crossing S (i.e., edges with exactly one endpoint in S). By designing an approximate kernel for Constrained Max-Cut and building on the correlation rounding technique of Raghavendra and Tan (2012), we present a (0.858 - ε)-approximation algorithm for the problem when c = O(1). The algorithm runs in time O(min{k/ε, n}^poly(c/ε) + poly(n)), where k = ∑_{i∈[c]} k_i and n = |V|. This improves upon the (1/2 + ε₀)-approximation of Feige and Langberg (2001) for Max-Cut_k (the special case when c = 1, k₁ = k), and generalizes the (0.858 - ε)-approximation of Raghavendra and Tan (2012), which only applies when min{k,n-k} = Ω(n) and does not handle multiple constraints. We also establish that, for general values of c, it is NP-hard to determine whether a feasible solution exists that cuts all edges. Finally, we present a 1/2-approximation algorithm for Max-Cut under an arbitrary matroid constraint.
Cite as

Yury Makarychev, Madhusudhan Reddy Pittu, and Ali Vakilian. Max-Cut with Multiple Cardinality Constraints. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{makarychev_et_al:LIPIcs.APPROX/RANDOM.2025.13,
  author =	{Makarychev, Yury and Pittu, Madhusudhan Reddy and Vakilian, Ali},
  title =	{{Max-Cut with Multiple Cardinality Constraints}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{13:1--13:21},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-243790},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.13},
  annote =	{Keywords: Maxcut, Semi-definite Programming, Sum of Squares Hierarchy}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.19
On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems

Authors: Ian DeHaan, Neng Huang, and Euiwoong Lee

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

Abstract
We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language Γ which has the dual discriminator operation as a polymorphism, there exists a |D|-approximation algorithm for MinCostCSP(Γ) where D is the domain. Complementing our algorithmic result, we show that any constraint language Γ where MinCostCSP(Γ) admits a constant-factor approximation must have a near-unanimity (NU) polymorphism unless P = NP, extending a similar result by Dalmau et al. on MinCSPs. These results imply a dichotomy of constant-factor approximability for constraint languages that contain all permutation relations (a natural generalization for Boolean CSPs that allow variable negation): either MinCostCSP(Γ) has an NU polymorphism and is |D|-approximable, or it does not have any NU polymorphism and is NP-hard to approximate within any constant factor. Finally, we present a constraint language which has a majority polymorphism, but is nonetheless NP-hard to approximate within any constant factor assuming the Unique Games Conjecture, showing that the condition of having an NU polymorphism is in general not sufficient unless UGC fails.
Cite as

Ian DeHaan, Neng Huang, and Euiwoong Lee. On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dehaan_et_al:LIPIcs.APPROX/RANDOM.2025.19,
  author =	{DeHaan, Ian and Huang, Neng and Lee, Euiwoong},
  title =	{{On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{19:1--19:24},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-243851},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.19},
  annote =	{Keywords: Constraint satisfaction problems, approximation algorithms, polymorphisms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.20
Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson

Authors: Jungho Ahn, Ian DeHaan, Eun Jung Kim, and Euiwoong Lee

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

Abstract
We present a polynomial-time (α_{GW} + ε)-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where α_{GW} ≈ 0.878 is the approximation guarantee of the Goemans-Williamson algorithm and ε > 10^{-34} is a fixed constant. To attain this, we give an improved analysis of a slight modification of the Goemans-Williamson algorithm for graphs in which triangles can be packed into a constant fraction of their edges. We then pair this analysis with structural results showing that both interval graphs and split graphs either have such a triangle packing or have maximum cut close to their number of edges. We also show that, subject to the Small Set Expansion Hypothesis, there exists a constant c > 0 such that there is no polyomial-time (1 - c)-approximation for Maximum Cut on split graphs.
Cite as

Jungho Ahn, Ian DeHaan, Eun Jung Kim, and Euiwoong Lee. Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ahn_et_al:LIPIcs.APPROX/RANDOM.2025.20,
  author =	{Ahn, Jungho and DeHaan, Ian and Kim, Eun Jung and Lee, Euiwoong},
  title =	{{Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{20:1--20:22},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-243869},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.20},
  annote =	{Keywords: Maximum cut, graph theory, interval graphs, split graphs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.10
Biased Linearity Testing in the 1% Regime

Authors: Subhash Khot and Kunal Mittal

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

Abstract
We study linearity testing over the p-biased hypercube ({0,1}ⁿ, μ_p^{⊗n}) in the 1% regime. For a distribution ν supported over {x ∈ {0,1}^k:∑_{i=1}^k x_i = 0 (mod 2)}, with marginal distribution μ_p in each coordinate, the corresponding k-query linearity test Lin(ν) proceeds as follows: Given query access to a function f:{0,1}ⁿ → {-1,1}, sample (x_1,… ,x_k)∼ ν^{⊗n}, query f on x_1,… ,x_k, and accept if and only if ∏_{i ∈ [k]} f(x_i) = 1. Building on the work of Bhangale, Khot, and Minzer (STOC '23), we show, for 0 < p ≤ 1/2, that if k ≥ 1+1/p, then there exists a distribution ν such that the test Lin(ν) works in the 1% regime; that is, any function f:{0,1}ⁿ → {-1,1} passing the test Lin(ν) with probability ≥ 1/2+ε, for some constant ε > 0, satisfies Pr_{x∼μ_p^{⊗n}}[f(x) = g(x)] ≥ 1/2+δ, for some linear function g, and a constant δ = δ(ε) > 0. Conversely, we show that if k < 1+1/p, then no such test Lin(ν) works in the 1% regime. Our key observation is that the linearity test Lin(ν) works if and only if the distribution ν satisfies a certain pairwise independence property.
Cite as

Subhash Khot and Kunal Mittal. Biased Linearity Testing in the 1% Regime. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khot_et_al:LIPIcs.CCC.2025.10,
  author =	{Khot, Subhash and Mittal, Kunal},
  title =	{{Biased Linearity Testing in the 1\% Regime}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.10},
  URN =		{urn:nbn:de:0030-drops-237046},
  doi =		{10.4230/LIPIcs.CCC.2025.10},
  annote =	{Keywords: Linearity test, 1\% regime, p-biased}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.34
Witness Encryption and NP-Hardness of Learning

Authors: Halley Goldberg and Valentine Kabanets

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

Abstract
We study connections between two fundamental questions from computer science theory. (1) Is witness encryption possible for NP [Sanjam Garg et al., 2013]? That is, given an instance x of an NP-complete language L, can one encrypt a secret message with security contingent on the ability to provide a witness for x ∈ L? (2) Is computational learning (in the sense of [Leslie G. Valiant, 1984; Michael J. Kearns et al., 1994]) hard for NP? That is, is there a polynomial-time reduction from instances of L to instances of learning? Our main contribution is that certain formulations of NP-hardness of learning characterize the existence of witness encryption for NP. More specifically, we show: - witness encryption for a language L ∈ NP is equivalent to a half-Levin reduction from L to the Computational Gap Learning problem (denoted CGL [Benny Applebaum et al., 2008]), where a half-Levin reduction is the same as a Levin reduction but only required to preserve witnesses in one direction, and CGL formalizes agnostic learning as a decision problem. We show versions of the statement above for witness encryption secure against non-uniform and uniform adversaries. We also show that witness encryption for NP with ciphertexts of logarithmic length, along with a circuit lower bound for E, are together equivalent to NP-hardness of a generalized promise version of MCSP. We complement the above with a number of unconditional NP-hardness results for agnostic PAC learning. Extending a result of [Shuichi Hirahara, 2022] to the standard setting of boolean circuits, we show NP-hardness of "semi-proper" learning. Namely: - for some polynomial s, it is NP-hard to agnostically learn circuits of size s(n) by circuits of size s(n)⋅ n^{1/(log log n)^O(1)}. Looking beyond the computational model of standard boolean circuits enables us to prove NP-hardness of improper learning (ie. without a restriction on the size of hypothesis returned by the learner). We obtain such results for: - learning circuits with oracle access to a given randomly sampled string, and - learning RAM programs. In particular, we show that a variant of MINLT [Ker-I Ko, 1991] for RAM programs is NP-hard with parameters corresponding to the setting of improper learning. We view these results as partial progress toward the ultimate goal of showing NP-hardness of learning boolean circuits in an improper setting. Lastly, we give some consequences of NP-hardness of learning for private- and public-key cryptography. Improving a main result of [Benny Applebaum et al., 2008], we show that if improper agnostic PAC learning is NP-hard under a randomized non-adaptive reduction (with some restrictions), then NP ⊈ BPP implies the existence of i.o. one-way functions. In contrast, if CGL is NP-hard under a half-Levin reduction, then NP ⊈ BPP implies the existence of i.o. public-key encryption.
Cite as

Halley Goldberg and Valentine Kabanets. Witness Encryption and NP-Hardness of Learning. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 34:1-34:43, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goldberg_et_al:LIPIcs.CCC.2025.34,
  author =	{Goldberg, Halley and Kabanets, Valentine},
  title =	{{Witness Encryption and NP-Hardness of Learning}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{34:1--34:43},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.34},
  URN =		{urn:nbn:de:0030-drops-237281},
  doi =		{10.4230/LIPIcs.CCC.2025.34},
  annote =	{Keywords: agnostic PAC learning, witness encryption, NP-hardness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.11
A Near-Optimal Polynomial Distance Lemma over Boolean Slices

Authors: Prashanth Amireddy, Amik Raj Behera, Srikanth Srinivasan, and Madhu Sudan

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

Abstract
The celebrated Ore-DeMillo-Lipton-Schwartz-Zippel (ODLSZ) lemma asserts that n-variate non-zero polynomial functions of degree d over a field 𝔽, are non-zero over any "grid" (points of the form Sⁿ for finite subset S ⊆ 𝔽) with probability at least max{|S|^{-d/(|S|-1)},1-d/|S|} over the choice of random point from the grid. In particular, over the Boolean cube (S = {0,1} ⊆ 𝔽), the lemma asserts non-zero polynomials are non-zero with probability at least 2^{-d}. In this work we extend the ODLSZ lemma optimally (up to lower-order terms) to "Boolean slices" i.e., points of Hamming weight exactly k. We show that non-zero polynomials on the slice are non-zero with probability (t/n)^{d}(1 - o_{n}(1)) where t = min{k,n-k} for every d ≤ k ≤ (n-d). As with the ODLSZ lemma, our results extend to polynomials over Abelian groups. This bound is tight upto the error term as evidenced by multilinear monomials of degree d, and it is also the case that some corrective term is necessary. A particularly interesting case is the "balanced slice" (k = n/2) where our lemma asserts that non-zero polynomials are non-zero with roughly the same probability on the slice as on the whole cube. The behaviour of low-degree polynomials over Boolean slices has received much attention in recent years. However, the problem of proving a tight version of the ODLSZ lemma does not seem to have been considered before, except for a recent work of Amireddy, Behera, Paraashar, Srinivasan and Sudan (SODA 2025), who established a sub-optimal bound of approximately ((k/n)⋅ (1-(k/n)))^d using a proof similar to that of the standard ODLSZ lemma. While the statement of our result mimics that of the ODLSZ lemma, our proof is significantly more intricate and involves spectral reasoning which is employed to show that a natural way of embedding a copy of the Boolean cube inside a balanced Boolean slice is a good sampler.
Cite as

Prashanth Amireddy, Amik Raj Behera, Srikanth Srinivasan, and Madhu Sudan. A Near-Optimal Polynomial Distance Lemma over Boolean Slices. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amireddy_et_al:LIPIcs.ICALP.2025.11,
  author =	{Amireddy, Prashanth and Behera, Amik Raj and Srinivasan, Srikanth and Sudan, Madhu},
  title =	{{A Near-Optimal Polynomial Distance Lemma over Boolean Slices}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.11},
  URN =		{urn:nbn:de:0030-drops-233881},
  doi =		{10.4230/LIPIcs.ICALP.2025.11},
  annote =	{Keywords: Low-degree polynomials, Boolean slices, Schwartz-Zippel Lemma}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.96
Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration

Authors: Shuichi Hirahara and Naoto Ohsaka

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

Abstract
k-Coloring Reconfiguration is one of the most well-studied reconfiguration problems, which asks to transform a given proper k-coloring of a graph to another by repeatedly recoloring a single vertex. Its approximate version, Maxmin k-Cut Reconfiguration, is defined as an optimization problem of maximizing the minimum fraction of bichromatic edges during the transformation between (not necessarily proper) k-colorings. In this paper, we demonstrate that the optimal approximation factor of this problem is 1 - Θ(1/k) for every k ≥ 2. Specifically, we prove the PSPACE-hardness of approximating the objective value within a factor of 1 - ε/k for some universal constant ε > 0, whereas we develop a deterministic polynomial-time algorithm that achieves the approximation factor of 1 - 2/k. To prove the hardness result, we propose a new probabilistic verifier that tests a "striped" pattern. Our approximation algorithm is based on a random transformation that passes through a random k-coloring.
Cite as

Shuichi Hirahara and Naoto Ohsaka. Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 96:1-96:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ICALP.2025.96,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto},
  title =	{{Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{96:1--96:18},
  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.2025.96},
  URN =		{urn:nbn:de:0030-drops-234733},
  doi =		{10.4230/LIPIcs.ICALP.2025.96},
  annote =	{Keywords: reconfiguration problems, graph coloring, hardness of approximation}
}
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