97 Search Results for "Rubinfeld, Ronitt"

Document
DOI: 10.4230/LIPIcs.STACS.2026.79
Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

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

Abstract
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.
Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  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.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.30
Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions

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

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

Abstract
Given Boolean functions f, g : 𝔽₂ⁿ → {-1,+1}, we say they are linearly isomorphic if there exists A ∈ GL_n(𝔽₂) such that f(x) = g(Ax) for all x. We study this problem in the tolerant property testing framework under the known-unknown model, where g is given explicitly and f is accessible only via oracle queries, meaning the algorithm may adaptively request the value of f(x) for inputs x ∈ 𝔽₂ⁿ of its choice. Given parameters ε ≥ 0 and ω > 0, the goal is to distinguish whether there exists A ∈ GL_n(𝔽₂) such that the normalized Hamming distance between f and g(Ax) is at most ε, or whether for every A ∈ GL_n(𝔽₂) the distance is at least ε+ω. Our main result is a tolerant tester making Õ ((m/ω) ⁴) queries to f, where m is an upper bound on the spectral norm of g, improving the previous Õ ((m/ω) ^{24}) bound of Wimmer and Yoshida. We complement this with a nearly matching lower bound of Ω(m²) for constant ω (for example, ω = 1/4), improving the prior Ω(log m) lower bound of Grigorescu, Wimmer and Xie. A key technical ingredient on the algorithmic side is a query-efficient local list corrector. For the lower bound, we give a reduction from communication complexity using a novel subclass of Maiorana-McFarland functions from symmetric-key cryptography.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{datta_et_al:LIPIcs.STACS.2026.30,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{30:1--30:21},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-255194},
  doi =		{10.4230/LIPIcs.STACS.2026.30},
  annote =	{Keywords: Boolean Function, Isomorphism of Boolean Function, Fourier Analysis, Sublinear Algorithm, Property Testing}
}
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.
Cite as

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.ITCS.2026.51
Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems

Authors: Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu

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

Abstract
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing notions of sparsification measure the level of sparsity, called degree, as the ratio of queried items to the optimal solution size. While effective for matching and matroid-type problems with uniform structures, this cardinality-based approach fails for knapsack-type constraints where feasible sets exhibit dramatic structural variation. We introduce a polyhedral sparsification framework that measures the degree as the smallest scalar needed to embed the query set within a scaled feasibility polytope, naturally capturing redundancy without relying on cardinality. Our main contribution establishes that knapsack, multiple knapsack, and generalized assignment problems admit (1-ε)-approximate sparsifiers with degree polynomial in 1/p and 1/ε - where p denotes the independent activation probability of each element - remarkably independent of problem dimensions. The key insight involves grouping items with similar weights and deploying a charging argument: when our query set misses an optimal item, we either substitute it directly with a queried item from the same group or leverage that group’s excess contribution to compensate for the loss. This reveals an intriguing complexity-theoretic separation - while the multiple knapsack problem lacks an FPTAS and generalized assignment is APX-hard, their sparsification counterparts admit efficient (1-ε)-approximation algorithms that identify polynomial degree query sets. Finally, we raise an open question: can such sparsification extend to general integer linear programs with degree independent of problem dimensions?
Cite as

Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu. Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 51:1-51:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dughmi_et_al:LIPIcs.ITCS.2026.51,
  author =	{Dughmi, Shaddin and Kalayci, Yusuf Hakan and Liu, Xinyu},
  title =	{{Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{51:1--51:22},
  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.2026.51},
  URN =		{urn:nbn:de:0030-drops-253386},
  doi =		{10.4230/LIPIcs.ITCS.2026.51},
  annote =	{Keywords: Packing Problems, Assignment Problems, Stochastic Selection, Sparsification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.103
A General Framework for Low Soundness Homomorphism Testing

Authors: Tushant Mittal and Sourya Roy

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

Abstract
We introduce a general framework to design and analyze algorithms for the problem of testing homomorphisms between finite groups in the low-soundness regime. In this regime, we give the first constant-query tests for various families of groups. These include tests for: (i) homomorphisms between arbitrary cyclic groups, (ii) homomorphisms between any finite group and ℤ_p, (iii) automorphisms of dihedral and symmetric groups, (iv) inner automorphisms of non-abelian finite simple groups and extraspecial groups, and (v) testing linear characters of GL_n(F_q), and finite-dimensional Lie algebras over F_q. We also recover the result of Kiwi [TCS'03] for testing homomorphisms between F_qⁿ and F_q. Prior to this work, such tests were only known for abelian groups with a constant maximal order (such as F_qⁿ). No tests were known for non-abelian groups. As an additional corollary, our framework gives combinatorial list decoding bounds for cyclic groups with list size dependence of O(ε^{-2}) (for agreement parameter ε). This improves upon the currently best-known bound of O(ε^{-105}) due to Dinur, Grigorescu, Kopparty, and Sudan [STOC'08], and Guo and Sudan [RANDOM'14].
Cite as

Tushant Mittal and Sourya Roy. A General Framework for Low Soundness Homomorphism Testing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 103:1-103:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mittal_et_al:LIPIcs.ITCS.2026.103,
  author =	{Mittal, Tushant and Roy, Sourya},
  title =	{{A General Framework for Low Soundness Homomorphism Testing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{103:1--103:18},
  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.2026.103},
  URN =		{urn:nbn:de:0030-drops-253901},
  doi =		{10.4230/LIPIcs.ITCS.2026.103},
  annote =	{Keywords: Property Testing, Coding Theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.54
Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space

Authors: Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan

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

Abstract
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the graph is bounded by some parameter ̅α. However, when this promise is violated, the estimates given by these algorithms are no longer guaranteed to be correct. For the triangle counting task, we give an algorithm that requires no promise on the input graph G, and computes a (1±ε)-approximation for the number of triangles t in G in time O^*((m⋅ α(G))/t + m/(t^{2/3)}), where α(G) is the arboricity of the graph. The algorithm can be used on any graph G (no prior knowledge of the arboricity α(G) is required), and the algorithm adapts its run-time on the fly based on the graph G. We accomplish this by trying a sequence of candidate values α̃ for α(G) and using a novel algorithm in the framework of testable algorithms. This ensures that wrong candidates α̃ cannot lead to wrong estimates: if the advice is incorrect, the algorithm either succeeds despite this or detects this and continues with a new candidate. Once the algorithm accepts the candidate, its output is guaranteed to be correct with high probability. We prove that this approach preserves - up to an additive overhead - the dramatic efficiency gains obtainable when good arboricity bounds are known in advance, while ensuring robustness against misleading advice. We further complement this result with a lower bound, showing that such an overhead is unavoidable whenever the advice may be faulty. We further demonstrate implications of our results for triangle counting in the streaming model.
Cite as

Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan. Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{eden_et_al:LIPIcs.ITCS.2026.54,
  author =	{Eden, Talya and Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{54:1--54:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.54},
  URN =		{urn:nbn:de:0030-drops-253417},
  doi =		{10.4230/LIPIcs.ITCS.2026.54},
  annote =	{Keywords: Sublinear Algorithms, Triangle Counting, Edge Counting, Arboricity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.53
Average Sensitivity of Geometric Algorithms

Authors: Matthijs Ebbens and Yuichi Yoshida

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

Abstract
In modern applications of geometric algorithms, it is often unrealistic to assume that the input representation fully captures all relevant aspects of the problem, because the input data is often large and dynamic. To address this challenge, we consider the notion of average sensitivity, which is defined as the average earth mover’s distance between the output distributions of the algorithm when run on an input and the same input with one point removed, where the average is over removed points and the distance between two outputs is measured using the symmetric difference size. We start by showing that a number of classical problems from computational geometry, in particular the convex hull, Delaunay triangulation, and Voronoi diagram problems, are "simple" from the viewpoint of average sensitivity by proving tight bounds for the average sensitivity of any algorithm for these problems. Then, we continue by constructing an algorithm with low average sensitivity that computes, for any ε > 0, a set of (1/3+ε)n guards for the art gallery problem. This is the main technical contribution of this work, which combines algorithms from computational geometry with results from the theory of local computation algorithms (LCAs) and property testing.
Cite as

Matthijs Ebbens and Yuichi Yoshida. Average Sensitivity of Geometric Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 53:1-53:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ebbens_et_al:LIPIcs.ITCS.2026.53,
  author =	{Ebbens, Matthijs and Yoshida, Yuichi},
  title =	{{Average Sensitivity of Geometric Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{53:1--53:16},
  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.2026.53},
  URN =		{urn:nbn:de:0030-drops-253409},
  doi =		{10.4230/LIPIcs.ITCS.2026.53},
  annote =	{Keywords: Average Sensitivity, Convex Hull, Delaunay Triangulation, Voronoi Diagram, Art Gallery}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

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

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.20
Samplability Makes Learning Easier

Authors: Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan

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

Abstract
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions - even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton 1993), where learners only have to succeed under samplable distributions. We study this distinction and show that samplable PAC substantially expands the power of efficient learners. We first construct a concept class that requires exponential sample complexity in standard PAC but is learnable with polynomial sample complexity in samplable PAC. We then lift this statistical separation to the computational setting and obtain a separation relative to a random oracle. Our proofs center around a new complexity primitive, explicit evasive sets, that we introduce and study. These are sets for which membership is easy to determine but are extremely hard to sample from. Our results extend to the online setting to similarly show that its landscape changes when the adversary is assumed to be efficient instead of computationally unbounded.
Cite as

Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan. Samplability Makes Learning Easier. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 20:1-20:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blanc_et_al:LIPIcs.ITCS.2026.20,
  author =	{Blanc, Guy and Koch, Caleb and Lange, Jane and Strassle, Carmen and Tan, Li-Yang},
  title =	{{Samplability Makes Learning Easier}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{20:1--20:12},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-253071},
  doi =		{10.4230/LIPIcs.ITCS.2026.20},
  annote =	{Keywords: PAC learning, Samplable distributions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.66
A Parameterized-Complexity Framework for Finding Local Optima

Authors: Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz

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

Abstract
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm problem, introduced by Johnson, Papadimitriou, and Yannakakis (1988) fail to capture the methodology of local search algorithms: PLS is concerned with finding a local optimum and not with using local search, while the standard algorithm problem restricts each improvement step to follow a fixed pivoting rule. In this work, we introduce a novel formulation of local search which provides a middle ground between these models. In particular, the task is to output not only a local optimum but also a chain of local improvements leading to it. With this framework, we aim to capture the challenge in designing a good pivoting rule. Especially, when combined with the parameterized complexity paradigm, it enables both strong lower bounds and meaningful tractability results. Unlike previous works that combined parameterized complexity with local search, our framework targets the whole task of finding a local optimum and not only a single improvement step. Focusing on two representative meta-problems - Subset Weight Optimization Problem with the c-swap neighborhood and Weighted Circuit with the flip neighborhood - we establish fixed-parameter tractability results related to the number of distinct weights, while ruling out an analogous result when parameterizing by the distance to the nearest optimum via a new type of reduction.
Cite as

Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz. A Parameterized-Complexity Framework for Finding Local Optima. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 66:1-66:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.ITCS.2026.66,
  author =	{Ganian, Robert and Hoang, Hung P. and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Parameterized-Complexity Framework for Finding Local Optima}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{66:1--66:20},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-253532},
  doi =		{10.4230/LIPIcs.ITCS.2026.66},
  annote =	{Keywords: Local Search, Parameterized Complexity, PLS}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.117
On the Power of Computationally Sound Interactive Proofs of Proximity

Authors: Hadar Strauss

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

Abstract
Interactive proofs of proximity (IPPs) are a relaxation of interactive proofs, analogous to property testing, in which soundness is required to hold only for inputs that are ε-far from the property being verified, where ε > 0 is a proximity parameter. In such proof systems, the verifier has oracle access to the input, and it engages in two types of activities before making its decision: querying the input oracle and communicating with the prover. The main objective is to achieve protocols where both the query and communication complexities are extremely low. In this work, we focus on computationally sound IPPs (cs-IPPs). We study their power in two aspects: - Query complexity: We show that, assuming the existence of collision-resistant hashing functions (CRHFs), any public-coin cs-IPP that has query complexity q can be transformed into a cs-IPP that makes only O(1/ε) queries, while increasing the communication complexity by roughly q. If we further assume the existence of a good computational PIR (private information retrieval) scheme, then a similar transformation holds for general (i.e., possibly private-coin) cs-IPPs. - Coordination: Aside from the low query complexity, the resulting cs-IPP has only minimal coordination between the verifier’s two activities. The general definition of IPPs allows the verifier to fully coordinate its interaction with the prover and its queries to the input oracle. Goldreich, Rothblum, and Skverer (ITCS 2023) introduced two restricted models of IPPs that are minimally coordinated: The pre-coordinated model, where no information flows between the querying and interacting activities, but they may use a common source of randomness, and the isolated model, where the two activities are fully independent, each operating with a separate source of randomness. Our transformation shows that (under the aforementioned computational assumptions) any cs-IPP can be made to be in the pre-coordinated model, while preserving its efficiency. Hence, pre-coordinated cs-IPPs are essentially as powerful as general cs-IPPs. In contrast, we show that cs-IPPs in the isolated model are extremely limited, offering almost no advantage over property testers. Specifically, extending on a result shown by Goldreich et al. for unconditionally sound IPPs in the isolated model, we show that if a property has a cs-IPP in the isolated model that makes q queries and uses c > 0 bits of communication, then it has a tester with query complexity O(c⋅ q).
Cite as

Hadar Strauss. On the Power of Computationally Sound Interactive Proofs of Proximity. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 117:1-117:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{strauss:LIPIcs.ITCS.2026.117,
  author =	{Strauss, Hadar},
  title =	{{On the Power of Computationally Sound Interactive Proofs of Proximity}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{117:1--117:9},
  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.2026.117},
  URN =		{urn:nbn:de:0030-drops-254047},
  doi =		{10.4230/LIPIcs.ITCS.2026.117},
  annote =	{Keywords: Interactive Proofs of Proximity, Computational Soundness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.33
Uniformity Testing Under User-Level Local Privacy

Authors: Clément L. Canonne, Abigail Gentle, and Vikrant Singhal

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

Abstract
We initiate the study of distribution testing under user-level local differential privacy, where each of n users contributes m samples from the unknown underlying distribution. This setting, albeit very natural, is significantly more challenging than the usual locally private setting, as for the same parameter ε the privacy guarantee must now apply to a full batch of m data points. While some recent work considers distribution learning in this user-level setting, nothing was known for even the most fundamental testing task, uniformity testing (and its generalization, identity testing). We address this gap, by providing (nearly) sample-optimal user-level LDP algorithms for uniformity and identity testing. Motivated by practical considerations, our main focus is on the private-coin, symmetric setting, which does not require users to share a common random seed nor to have been assigned a globally unique identifier.
Cite as

Clément L. Canonne, Abigail Gentle, and Vikrant Singhal. Uniformity Testing Under User-Level Local Privacy. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{canonne_et_al:LIPIcs.ITCS.2026.33,
  author =	{Canonne, Cl\'{e}ment L. and Gentle, Abigail and Singhal, Vikrant},
  title =	{{Uniformity Testing Under User-Level Local Privacy}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.33},
  URN =		{urn:nbn:de:0030-drops-253201},
  doi =		{10.4230/LIPIcs.ITCS.2026.33},
  annote =	{Keywords: Differential Privacy, Local Differential Privacy, Uniformity Testing, Identity Testing, Hypothesis Testing, User-Level Differential Privacy, Person-Level Differential Privacy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.34
Testing Classical Properties from Quantum Data

Authors: Matthias C. Caro, Preksha Naik, and Joseph Slote

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

Abstract
Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of f instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |f⟩∝ ∑_x|x,f(x)⟩ or the phase state |(-1)^f⟩∝ ∑_x (-1)^{f(x)}|x⟩. Quantum advantage in testing from data. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query-based testers in each case. Inadequacy of Fourier sampling. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2^{Ω(n)} for any tester relying exclusively on Fourier and classical samples. Classical queries vs. quantum data. Our passive quantum testers are competitive with classical query-based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2^{n/2}) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. Towards lower bounds. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.
Cite as

Matthias C. Caro, Preksha Naik, and Joseph Slote. Testing Classical Properties from Quantum Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2026.34,
  author =	{Caro, Matthias C. and Naik, Preksha and Slote, Joseph},
  title =	{{Testing Classical Properties from Quantum Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{34:1--34:26},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-253213},
  doi =		{10.4230/LIPIcs.ITCS.2026.34},
  annote =	{Keywords: Quantum Property Testing, Quantum Data, Boolean Functions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.18
Interactive Proofs for Distribution Testing with Conditional Oracles

Authors: Ari Biswas, Mark Bun, Clément L. Canonne, and Satchit Sivakumar

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

Abstract
We revisit the framework of interactive proofs for distribution testing, first introduced by Chiesa and Gur (ITCS 2018), which has recently experienced a surge in interest, accompanied by notable progress (e.g., Herman and Rothblum, STOC 2022, FOCS 2023; Herman, RANDOM 2024). In this model, a data-poor verifier determines whether a probability distribution has a property of interest by interacting with an all-powerful, data-rich but untrusted prover bent on convincing them that it has the property. While prior work gave sample-, time-, and communication-efficient protocols for testing and estimating a range of distribution properties, they all suffer from an inherent issue: for most interesting properties of distributions over a domain of size N, the verifier must draw at least Ω(√N) samples of its own. While sublinear in N, this is still prohibitive for large domains encountered in practice. In this work, we circumvent this limitation by augmenting the verifier with the ability to perform an exponentially smaller number of more powerful (but reasonable) pairwise conditional queries, effectively enabling them to perform "local comparison checks" of the prover’s claims. We systematically investigate the landscape of interactive proofs in this new setting, giving poly-logarithmic query and sample protocols for (tolerantly) testing all label-invariant properties, thus demonstrating exponential savings without compromising on communication, for this large and fundamental class of testing tasks.
Cite as

Ari Biswas, Mark Bun, Clément L. Canonne, and Satchit Sivakumar. Interactive Proofs for Distribution Testing with Conditional Oracles. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{biswas_et_al:LIPIcs.ITCS.2026.18,
  author =	{Biswas, Ari and Bun, Mark and Canonne, Cl\'{e}ment L. and Sivakumar, Satchit},
  title =	{{Interactive Proofs for Distribution Testing with Conditional Oracles}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{18:1--18:13},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-253059},
  doi =		{10.4230/LIPIcs.ITCS.2026.18},
  annote =	{Keywords: Distribution Testing, Interactive Proofs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.89
On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time

Authors: Tsz Chiu Kwok, Zhewei Wei, and Mingji Yang

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

Abstract
We initiate a study of solving a row/column diagonally dominant (RDD/CDD) linear system 𝐌x = b in sublinear time, with the goal of estimating t^{⊤}x^{∗} for a given vector t ∈ ℝⁿ and a specific solution x^{∗}. This setting naturally generalizes the study of sublinear-time solvers for symmetric diagonally dominant (SDD) systems [Andoni-Krauthgamer-Pogrow, ITCS 2019] to the asymmetric case, which has remained underexplored despite extensive work on nearly-linear-time solvers for RDD/CDD systems. Our first contributions are characterizations of the problem’s mathematical structure. We express a solution x^{∗} via a Neumann series, prove its convergence, and upper bound the truncation error on this series through a novel quantity of 𝐌, termed the maximum p-norm gap. This quantity generalizes the spectral gap of symmetric matrices and captures how the structure of 𝐌 governs the problem’s computational difficulty. For systems with bounded maximum p-norm gap, we develop a collection of algorithmic results for locally approximating t^{⊤}x^{∗} under various scenarios and error measures. We derive these results by adapting the techniques of random-walk sampling, local push, and their bidirectional combination, which have proved powerful for special cases of solving RDD/CDD systems, particularly estimating PageRank and effective resistance on graphs. Our general framework yields deeper insights, extended results, and improved complexity bounds for these problems. Notably, our perspective provides a unified understanding of Forward Push and Backward Push, two fundamental approaches for estimating random-walk probabilities on graphs. Our framework also inherits the hardness results for sublinear-time SDD solvers and local PageRank computation, establishing lower bounds on the maximum p-norm gap or the accuracy parameter. We hope that our work opens the door for further study into sublinear solvers, local graph algorithms, and directed spectral graph theory.
Cite as

Tsz Chiu Kwok, Zhewei Wei, and Mingji Yang. On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 89:1-89:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kwok_et_al:LIPIcs.ITCS.2026.89,
  author =	{Kwok, Tsz Chiu and Wei, Zhewei and Yang, Mingji},
  title =	{{On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{89:1--89:25},
  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.2026.89},
  URN =		{urn:nbn:de:0030-drops-253768},
  doi =		{10.4230/LIPIcs.ITCS.2026.89},
  annote =	{Keywords: Spectral Graph Theory, Linear Systems, Sublinear Algorithms}
}
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