40 Search Results for "Diakonikolas, Ilias"

Document
DOI: 10.4230/LIPIcs.SEA.2026.21
An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem

Authors: Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
In this paper, we perform an experimental study of approximation algorithms for the unweighted tree augmentation problem (UTAP). Our goal is to establish a baseline performance for several existing approximation algorithms on actual instances rather than worst-case instances. In particular, we are interested in whether the algorithms' performance in practical instances is consistent with their worst-case guarantee rankings. We are also interested in whether preprocessing times, implementation difficulties, and running times justify the use of an algorithm in practice. We profile and analyze three approximation algorithms from the literature against a simple randomized algorithm. The performance of each algorithm was evaluated using metrics for space usage, running time, and solution quality. We found that the simple randomized algorithm is very competitive with the approximation algorithms and that the algorithms do not necessarily rank according to their theoretical guarantees. The randomized algorithm is easier to implement and understand, using less space than any of the more sophisticated approximation algorithms.
Cite as

Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler. An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hawranick_et_al:LIPIcs.SEA.2026.21,
  author =	{Hawranick, Luke and Williamson, Matthew and Restanio, Jacob and Subramani, K. and Klingler, Cody},
  title =	{{An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.21},
  URN =		{urn:nbn:de:0030-drops-260259},
  doi =		{10.4230/LIPIcs.SEA.2026.21},
  annote =	{Keywords: Graphs, Networks, Tree Augmentation, Approximation Algorithms, Empirical}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.33
The Smallest String Attractors of Fibonacci and Period-Doubling Words

Authors: Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
A string attractor of a string T[1..|T|] is a set of positions Γ of T such that any substring w of T has an occurrence that crosses a position in Γ, i.e., there is a position i such that w = T[i..i+|w|-1] and the intersection [i,i+|w|-1]∩ Γ is nonempty. The size of the smallest string attractor of Fibonacci words is known to be 2. We completely characterize the set of all smallest string attractors of Fibonacci words, and show a recursive formula describing the 2^{n-4} + 2^{⌈n/2⌉ - 2} distinct position pairs that are the smallest string attractors of the nth Fibonacci word for n ≥ 7. Similarly, the size of the smallest string attractor of period-doubling words is known to be 2. We also completely characterize the set of all smallest string attractors of period-doubling words, and show a formula describing the two distinct position pairs that are the smallest string attractors of the nth period-doubling word for n ≥ 2. Our results show that strings with the same smallest attractor size can have a drastically different number of distinct smallest attractors.
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Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto. The Smallest String Attractors of Fibonacci and Period-Doubling Words. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{banbara_et_al:LIPIcs.CPM.2026.33,
  author =	{Banbara, Mutsunori and Bannai, Hideo and Guo, Peaker and K\"{o}ppl, Dominik and Mieno, Takuya and Okamoto, Yoshio},
  title =	{{The Smallest String Attractors of Fibonacci and Period-Doubling Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.33},
  URN =		{urn:nbn:de:0030-drops-259599},
  doi =		{10.4230/LIPIcs.CPM.2026.33},
  annote =	{Keywords: String attractors, Fibonacci words, Period-doubling words, Combinatorics on words}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.19
Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means

Authors: Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is equipped with a protected attribute, and a number k, the goal is to partition P into k clusters with a designated center each, such that a center-based objective function is minimized and the attributes are fairly distributed with respect to the following two fairness concepts: 1) group fairness: We aim for clusters with balanced numbers of attributes by specifying lower and upper bounds for the desired attribute proportions. 2) diverse center selection: Clusters have natural representatives, i.e., their centers. We ask for a balanced set of representatives by specifying the desired number of centers to choose from each attribute. Dickerson, Esmaeili, Morgenstern, and Pena [John P. Dickerson et al., 2023] denote the combination of these two constraints as doubly constrained fair clustering. They present algorithms whose guarantees depend on the best known approximation factors for either of these problems. Currently, this implies an 8-approximation with a small additive violation on the group fairness constraint. For k-center, we improve this approximation factor to 4 with a small additive violation. This guarantee also depends on the currently best algorithm for DS-fair k-center given by Jones, Nguyen and Nguyen [Matthew Jones et al., 2020]. For k-median and k-means, we propose the first constant-factor approximation algorithms. Our algorithms transform a solution that satisfies diverse center selection into a doubly constrained fair clustering using an LP-based approach. Furthermore, our results are generalizable to other center-selection constraints, such as matroid k-clustering and knapsack constraints.
Cite as

Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm. Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{funk_et_al:LIPIcs.SWAT.2026.19,
  author =	{Funk, Nicole and Hennes, Annika and Hillebrand, Johanna and Sturm, Sarah},
  title =	{{Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.19},
  URN =		{urn:nbn:de:0030-drops-260551},
  doi =		{10.4230/LIPIcs.SWAT.2026.19},
  annote =	{Keywords: Clustering, Fairness, Approximation Algorithms, k-center, k-median, k-means}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.17
Fréchet Distance in the Imbalanced Case

Authors: Lotte Blank

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Given two polygonal curves P and Q defined by n and m vertices with m ≤ n, we show that the discrete Fréchet distance in 1D cannot be approximated within a factor of 2-ε in 𝒪((nm)^{1-δ}) time for any ε, δ > 0 unless OVH fails. Using a similar construction, we extend this bound for curves in 2D under the continuous or discrete Fréchet distance and increase the approximation factor to 1+√2-ε (resp. 3-ε) if the curves lie in the Euclidean space (resp. in the L_∞-space). This strengthens the lower bound by Buchin, Ophelders, and Speckmann to the case where m = n^α for α ∈ (0,1) and increases the approximation factor of 1.001 by Bringmann. For the discrete Fréchet distance in 1D, we provide an approximation algorithm with optimal approximation factor and almost optimal running time. Further, for curves in any dimension embedded in any L_p space, we present a (3+ε)-approximation algorithm for the continuous and discrete Fréchet distance using 𝒪((n+m²)log n) time, which almost matches the approximation factor of the lower bound for the L_∞ metric.
Cite as

Lotte Blank. Fréchet Distance in the Imbalanced Case. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blank:LIPIcs.SoCG.2026.17,
  author =	{Blank, Lotte},
  title =	{{Fr\'{e}chet Distance in the Imbalanced Case}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.17},
  URN =		{urn:nbn:de:0030-drops-258232},
  doi =		{10.4230/LIPIcs.SoCG.2026.17},
  annote =	{Keywords: Fr\'{e}chet distance, SETH, Orthogonal Vectors, Lower Bounds, distance oracle, data structures}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.80
Hardness of High-Dimensional Linear Classification

Authors: Alexander Munteanu, Simon Omlor, and Jeff M. Phillips

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and approximate forms. However, only O(n^d) and respectively Õ(1/ε^d) upper bounds are known and complemented by polynomial lower bounds that do not support the exponential in dimension dependence. We close this gap up to polylogarithmic terms by reduction from widely-believed hardness conjectures for Affine Degeneracy testing and k-Sum problems. Our reductions yield matching lower bounds of Ω̃(n^d) and respectively Ω̃(1/ε^d) based on Affine Degeneracy testing, and Ω̃(n^{d/2}) and respectively Ω̃(1/ε^{d/2}) conditioned on k-Sum. The first bound also holds unconditionally if the computational model is restricted to make sidedness queries, which corresponds to a widely spread setting implemented and optimized in many contemporary algorithms and computing paradigms.
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Alexander Munteanu, Simon Omlor, and Jeff M. Phillips. Hardness of High-Dimensional Linear Classification. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 80:1-80:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{munteanu_et_al:LIPIcs.SoCG.2026.80,
  author =	{Munteanu, Alexander and Omlor, Simon and Phillips, Jeff M.},
  title =	{{Hardness of High-Dimensional Linear Classification}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{80:1--80:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.80},
  URN =		{urn:nbn:de:0030-drops-258871},
  doi =		{10.4230/LIPIcs.SoCG.2026.80},
  annote =	{Keywords: Conditional Hardness, k-Sum, Affine Degeneracy, Halfspace Discrepancy, Classification}
}
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.ITCS.2026.75
Prior-Independent and Subgame Optimal Online Algorithms

Authors: Jason Hartline, Aleck Johnsen, and Anant Shah

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

Abstract
This paper develops two game-theoretic notions of beyond worst-case analysis that give better than worst-case guarantees on natural inputs. We illustrate them through the finite-horizon ski-rental problem. First, we consider prior-independent design and analysis of online algorithms where, rather than choosing a worst-case input, the adversary chooses a worst-case independent and identical distribution over inputs. Prior-independent online algorithms are generally analytically intractable; instead we give a fully polynomial-time approximation scheme to compute them. Second, we consider the worst-case design of algorithms. We define "subgame optimality" which is stronger than worst-case optimality in that it requires the algorithm to take advantage of an adversary not playing a worst-case input. Algorithms that focus only on the worst case can be far from subgame optimal. Highlighting the potential improvement from these paradigms for the finite-horizon ski-rental problem, we empirically compare worst-case, subgame optimal, and prior-independent algorithms in the prior-independent framework. Finally, we analyze the structure of their decisions across input sequences: the prior-independent algorithm exhibits more extreme adaptations to observed data, in contrast with the more conservative behavior of worst-case and subgame optimal algorithms.
Cite as

Jason Hartline, Aleck Johnsen, and Anant Shah. Prior-Independent and Subgame Optimal Online Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hartline_et_al:LIPIcs.ITCS.2026.75,
  author =	{Hartline, Jason and Johnsen, Aleck and Shah, Anant},
  title =	{{Prior-Independent and Subgame Optimal Online Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{75:1--75:23},
  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.2026.75},
  URN =		{urn:nbn:de:0030-drops-253622},
  doi =		{10.4230/LIPIcs.ITCS.2026.75},
  annote =	{Keywords: online algorithms, prior-independent algorithm design, zero-sum games}
}
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.2026.33
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.2026.18
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.2026.86
The Secretary Problem with Predictions and a Chosen Order

Authors: Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco

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

Abstract
We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023). In this variant, the decision-maker has access to machine-learned predictions of candidate values in advance. The key challenge is to balance consistency and robustness: when the predictions are accurate, the algorithm should hire a near-best secretary; however, if they are inaccurate, the algorithm should still achieve a bounded competitive ratio. We consider both the standard Random Order Secretary Problem (ROSP), where candidates arrive in a uniform random order, and a more natural model in the learning-augmented setting, where the decision-maker can choose the arrival order based on the predicted candidate values. This model, which we call the Chosen Order Secretary Problem (COSP), can capture scenarios such as an interview schedule that is set by the decision-maker. We propose a novel algorithm that applies to both ROSP and COSP. Building on the approach of Fujii and Yoshida, our method switches from fully trusting predictions to a threshold-based rule when a large deviation of a prediction is observed. Importantly, unlike the algorithm of Fujii and Yoshida, our algorithm uses randomization as part of its decision logic. We show that if ε ∈ [0,1] denotes the maximum multiplicative prediction error, then for ROSP our algorithm achieves competitive ratio max {0.221, (1-ε)/(1+ε)}, improving on a previous bound of max {0.215, (1-ε)/(1+ε)} due to Fujii and Yoshida [Fujii and Yoshida, 2023]. For COSP, our algorithm achieves max {0.262, (1-ε)/(1+ε)}. This surpasses a 0.25 upper bound on the worst-case competitive ratio that applies to the approach of Fujii and Yoshida, and gets closer to the classical secretary benchmark of 1/e ≈ 0.368, which is an upper bound for any algorithm. Our result for COSP highlights the benefit of integrating predictions with arrival-order control in online decision-making.
Cite as

Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco. The Secretary Problem with Predictions and a Chosen Order. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 86:1-86:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karisani_et_al:LIPIcs.ITCS.2026.86,
  author =	{Karisani, Helia and Daneshvaramoli, Mohammadreza and Beyhaghi, Hedyeh and Hajiesmaili, Mohammad and Musco, Cameron},
  title =	{{The Secretary Problem with Predictions and a Chosen Order}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{86:1--86:24},
  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.2026.86},
  URN =		{urn:nbn:de:0030-drops-253734},
  doi =		{10.4230/LIPIcs.ITCS.2026.86},
  annote =	{Keywords: Secretary problem, learning-augmented algorithms, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.91
Limitations of Membership Queries in Testable Learning

Authors: Jane Lange and Mingda Qiao

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

Abstract
Membership queries (MQ) often yield speedups for learning tasks, particularly in the distribution-specific setting. We show that in the testable learning model of Rubinfeld and Vasilyan [Rubinfeld and Vasilyan, 2023], membership queries cannot decrease the time complexity of testable learning algorithms beyond the complexity of sample-only distribution-specific learning. In the testable learning model, the learner must output a hypothesis whenever the data distribution satisfies a desired property, and if it outputs a hypothesis, the hypothesis must be near-optimal. We give a general reduction from sample-based refutation of boolean concept classes, as presented in [Vadhan, 2017; Kothari and Livni, 2018], to testable learning with queries (TL-Q). This yields lower bounds for TL-Q via the reduction from learning to refutation given in [Kothari and Livni, 2018]. The result is that, relative to a concept class and a distribution family, no m-sample TL-Q algorithm can be super-polynomially more time-efficient than the best m-sample PAC learner. Finally, we define a class of "statistical" MQ algorithms that encompasses many known distribution-specific MQ learners, such as those based on influence estimation or subcube-conditional statistical queries. We show that TL-Q algorithms in this class imply efficient statistical-query refutation and learning algorithms. Thus, combined with known SQ dimension lower bounds, our results imply that these efficient membership query learners cannot be made testable.
Cite as

Jane Lange and Mingda Qiao. Limitations of Membership Queries in Testable Learning. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 91:1-91:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lange_et_al:LIPIcs.ITCS.2026.91,
  author =	{Lange, Jane and Qiao, Mingda},
  title =	{{Limitations of Membership Queries in Testable Learning}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{91:1--91:23},
  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.2026.91},
  URN =		{urn:nbn:de:0030-drops-253785},
  doi =		{10.4230/LIPIcs.ITCS.2026.91},
  annote =	{Keywords: Testable learning, PAC learning}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.37
Towards Optimal Distributed Edge Coloring with Fewer Colors

Authors: Manuel Jakob, Yannic Maus, and Florian Schager

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem: while (2Δ-1)-edge coloring - where Δ is the maximum degree - can be solved in 𝒪(log^{∗}(n)) rounds on constant-degree graphs, the seemingly minor reduction to (2Δ-2) colors leads to an Ω(log n) lower bound [Chang, He, Li, Pettie & Uitto, SODA'18]. Understanding this sharp divide between very local problems and inherently more global ones remains a central open question in distributed computing and it is a core focus of this paper. As our main contribution we design a deterministic distributed 𝒪(log n)-round reduction from the (2Δ-2)-edge coloring problem to the much easier (2Δ-1)-edge coloring problem. This reduction is optimal, as the (2Δ-2)-edge coloring problem admits an Ω(log n) lower bound that even holds on the class of constant-degree graphs, whereas the 2Δ-1-edge coloring problem can be solved in 𝒪(log^{∗}n) rounds. By plugging in the (2Δ-1)-edge coloring algorithms from [Balliu, Brandt, Kuhn & Olivetti, PODC'22] running in 𝒪(log^{12}Δ + log^{∗} n) rounds, we obtain an optimal runtime of 𝒪(log n) rounds as long as Δ = 2^{𝒪(log^{1/12} n)}. Previously, such an optimal algorithm was only known for the class of constant-degree graphs [Brandt, Maus, Narayanan, Schager & Uitto, SODA'25]. Furthermore, on general graphs our reduction improves the runtime from 𝒪̃(log³ n) to 𝒪̃(log^{5/3} n). In addition, we also obtain an optimal 𝒪(log log n)-round randomized reduction of (2Δ - 2)-edge coloring to (2Δ - 1)-edge coloring. This leads to a 𝒪̃(log^{5/3} log n)-round (2Δ-2)-edge coloring algorithm, which beats the (very recent) previous state-of-the-art taking 𝒪̃(log^{8/3}log n) rounds from [Bourreau, Brandt & Nolin, STOC'25]. Lastly, we obtain an 𝒪(log_Δ n)-round reduction from the (2Δ-1)-edge coloring, albeit to the somewhat harder maximal independent set (MIS) problem.
Cite as

Manuel Jakob, Yannic Maus, and Florian Schager. Towards Optimal Distributed Edge Coloring with Fewer Colors. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 37:1-37:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jakob_et_al:LIPIcs.DISC.2025.37,
  author =	{Jakob, Manuel and Maus, Yannic and Schager, Florian},
  title =	{{Towards Optimal Distributed Edge Coloring with Fewer Colors}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.37},
  URN =		{urn:nbn:de:0030-drops-248547},
  doi =		{10.4230/LIPIcs.DISC.2025.37},
  annote =	{Keywords: distributed graph algorithms, edge coloring, LOCAL model}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.18
Complexity Landscape for Local Certification

Authors: Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have an optimal algorithm with that complexity). In this paper, we initiate the study of the landscape for space complexity of distributed graph algorithms. More precisely, we focus on the local certification setting, where a prover assigns certificates to nodes to certify a property, and where the space complexity is measured by the size of the certificates. Already for anonymous paths and cycles, we unveil a surprising landscape: - There is a gap between complexity O(1) and Θ(log log n) in paths. This is the first gap established in local certification. - There exists a property that has complexity Θ(log log n) in paths, a regime that was not known to exist for a natural property. - There is a gap between complexity O(1) and Θ(log n) in cycles, hence a gap that is exponentially larger than for paths. We then generalize our result for paths to the class of trees. Namely, we show that there is a gap between complexity O(1) and Θ(log log d) in trees, where d is the diameter. We finally describe some settings where there are no gaps at all. To prove our results we develop a new toolkit, based on various results of automata theory and arithmetic, which is of independent interest.
Cite as

Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun. Complexity Landscape for Local Certification. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.DISC.2025.18,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Zeitoun, S\'{e}bastien},
  title =	{{Complexity Landscape for Local Certification}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.18},
  URN =		{urn:nbn:de:0030-drops-248350},
  doi =		{10.4230/LIPIcs.DISC.2025.18},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, space complexity, distributed graph algorithms, complexity gap}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.12
Distributed Computation with Local Advice

Authors: Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
Algorithms with advice have received ample attention in the distributed and online settings, and they have recently proven useful also in dynamic settings. In this work we study local computation with advice: the goal is to solve a graph problem Π with a distributed algorithm in T(Δ) communication rounds, for some function T that only depends on the maximum degree Δ of the graph, and the key question is how many bits of advice per node are needed. Some of our results regard Locally Checkable Labeling problems (LCLs), which is an important family of problems that includes various coloring and orientation problems on finite-degree graphs. These are constraint-satisfaction graph problems that can be defined with a finite set of valid input/output-labeled neighborhoods. Our main results are: 1) Any locally checkable labeling problem can be solved with only 1 bit of advice per node in graphs with sub-exponential growth (the number of nodes within radius r is sub-exponential in r; for example, grids are such graphs). Moreover, we can make the set of nodes that carry advice bits arbitrarily sparse. As a corollary, any locally checkable labeling problem admits a locally checkable proof with 1 bit per node in graphs with sub-exponential growth. 2) The assumption of sub-exponential growth is complemented by a conditional lower bound: assuming the Exponential-Time Hypothesis, there are locally checkable labeling problems that cannot be solved in general with any constant number of bits per node. 3) In any graph we can find an almost-balanced orientation (indegrees and outdegrees differ by at most one) with 1 bit of advice per node, and again we can make the advice arbitrarily sparse. As a corollary, we can also compress an arbitrary subset of edges so that a node of degree d stores only d/2 + 2 bits, and we can decompress it locally, in T(Δ) rounds. 4) In any graph of maximum degree Δ, we can find a Δ-coloring (if it exists) with 1 bit of advice per node, and again, we can make the advice arbitrarily sparse. 5) In any 3-colorable graph, we can find a 3-coloring with 1 bit of advice per node. As a corollary, in bounded-degree graphs there is a locally checkable proof that certifies 3-colorability with 1 bit of advice per node, while prior work shows that this is not possible with a proof labeling scheme (PLS), which is a more restricted setting where the verifier can only see up to distance 1. Our work shows that for many problems the key threshold is not whether we can achieve 1 bit of advice per node, but whether we can make the advice arbitrarily sparse. To formalize this idea, we develop a general framework of composable schemas that enables us to build algorithms for local computation with advice in a modular fashion: once we have (1) a schema for solving Π₁ and (2) a schema for solving Π₂ assuming an oracle for Π₁, we can also compose them and obtain (3) a schema that solves Π₂ without the oracle. It turns out that many natural problems admit composable schemas, all of them can be solved with only 1 bit of advice, and we can make the advice arbitrarily sparse.
Cite as

Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela. Distributed Computation with Local Advice. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.12,
  author =	{Balliu, Alkida and Brandt, Sebastian and Kuhn, Fabian and Nowicki, Krzysztof and Olivetti, Dennis and Rotenberg, Eva and Suomela, Jukka},
  title =	{{Distributed Computation with Local Advice}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.12},
  URN =		{urn:nbn:de:0030-drops-248295},
  doi =		{10.4230/LIPIcs.DISC.2025.12},
  annote =	{Keywords: Distributed graph algorithms, LOCAL model, computation with advice, locally checkable labeling problems, proof labeling schemes, locally checkable proofs, graph coloring, exponential-time hypothesis}
}
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