47 Search Results for "Yoshida, Yuichi"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.22
Search-Space Reduction for Boolean MinCSPs via Essential Constraints

Authors: Bart M. P. Jansen and Ruben F. A. Verhaegh

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

Abstract
For a fixed set ℱ of Boolean constraint types, a MinCSP(ℱ)-instance consists of a formula F that applies m constraints from ℱ to a set of n Boolean variables. The goal is to remove a minimum subset of constraint applications from F to make the remaining formula satisfiable. Previous work characterized how the choice of ℱ affects its polynomial-time solvability and approximability. We extend a recently introduced preprocessing framework for graph problems to the problem above. Rephrased in the context of CSPs, this framework defines a constraint application from a given formula F as c-essential if it is contained in all c-approximate solutions to F. Being able to efficiently detect these essential parts of a solution reduces the search space of any follow-up FPT algorithms parameterized by the solution size and yields an immediate asymptotic improvement to the runtime of such algorithms. In this work, we present a dichotomy theorem that distinguishes constraint sets ℱ for which c_ℱ-essential constraint applications can be detected efficiently for some c_{ℱ} ∈ 𝒪(1), from those for which this task is intractable under established complexity-theoretic conjectures. Our results show that for any set ℱ of bijunctive constraints, there is a polynomial-time algorithm that detects 𝒪(1)-essential constraint applications. This contrasts the fact that constant-factor approximating a bijunctive MinCSP(ℱ)-problem is intractable under the Unique Games Conjecture.
Cite as

Bart M. P. Jansen and Ruben F. A. Verhaegh. Search-Space Reduction for Boolean MinCSPs via Essential Constraints. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jansen_et_al:LIPIcs.SWAT.2026.22,
  author =	{Jansen, Bart M. P. and Verhaegh, Ruben F. A.},
  title =	{{Search-Space Reduction for Boolean MinCSPs via Essential Constraints}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{22:1--22:17},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-260586},
  doi =		{10.4230/LIPIcs.SWAT.2026.22},
  annote =	{Keywords: fixed-parameter tractability, constraint satisfaction problems}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.34
Linear-Time Exact Computation of Influence Spread on Bounded-Pathwidth Graphs

Authors: Kengo Nakamura and Masaaki Nishino

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

Abstract
Given a network and a set of vertices called seeds to initially inject information, influence spread is the expected number of vertices that eventually receive the information under a certain stochastic model of information propagation. Under the commonly used independent cascade model, influence spread is equivalent to the expected number of vertices reachable from the seeds on a directed uncertain graph, and the exact evaluation of influence spread offers many applications, e.g., influence maximization. Although its evaluation is a #P-hard task, there is an algorithm that can precisely compute the influence spread in O(mnω_p²⋅ 2^{ω_p²}) time, where ω_p is the pathwidth of the graph. We improve this by developing an algorithm that computes the influence spread in O((m+n)ω_p²⋅ 2^{ω_p²}) time. This is achieved by identifying the similarities in the repetitive computations in the existing algorithm and sharing them to reduce computation. Although similar refinements have been considered for the probability computation on undirected uncertain graphs, a greater number of similarities must be leveraged for directed graphs to achieve linear time complexity.
Cite as

Kengo Nakamura and Masaaki Nishino. Linear-Time Exact Computation of Influence Spread on Bounded-Pathwidth Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{nakamura_et_al:LIPIcs.SWAT.2026.34,
  author =	{Nakamura, Kengo and Nishino, Masaaki},
  title =	{{Linear-Time Exact Computation of Influence Spread on Bounded-Pathwidth Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{34:1--34:17},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-260704},
  doi =		{10.4230/LIPIcs.SWAT.2026.34},
  annote =	{Keywords: Influence spread, bounded pathwidth, network reliability, linear time algorithm}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.6
Ferry Cover with Connectivity Constraints

Authors: Niranjan Balachandran, Ankita Dargad, Urban Larsson, Neeldhara Misra, and Umesh Shankar

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
The classical Ferry Cover problem asks for the minimum boat capacity needed to transport all vertices of a graph across a river such that no edge remains on either bank at any time - a requirement that the banks induce stable (independent) sets. We study a natural generalization in which the banks must satisfy an arbitrary graph property. For hereditary properties such as acyclicity or planarity, we show that the structural characterization of small-boat and large-boat graphs established by Csorba, Hurkens, and Woeginger extends directly. We then turn to the connected-bank variant, where the property of interest - connectedness - is not hereditary: both banks must induce connected subgraphs throughout the transfer. We provide a complete characterization of graphs that can be transferred with a boat of size one (boat-1 graphs): a connected graph is boat-1 if and only if its block-cut tree is a path. This characterization yields a linear-time recognition algorithm. As a consequence, we show that every biconnected graph is boat-1, since such graphs admit an st-numbering. We also develop an efficient algorithm for determining the boat number of trees. Our work opens new directions for river-crossing problems under non-hereditary bank constraints.
Cite as

Niranjan Balachandran, Ankita Dargad, Urban Larsson, Neeldhara Misra, and Umesh Shankar. Ferry Cover with Connectivity Constraints. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{balachandran_et_al:LIPIcs.FUN.2026.6,
  author =	{Balachandran, Niranjan and Dargad, Ankita and Larsson, Urban and Misra, Neeldhara and Shankar, Umesh},
  title =	{{Ferry Cover with Connectivity Constraints}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.6},
  URN =		{urn:nbn:de:0030-drops-257253},
  doi =		{10.4230/LIPIcs.FUN.2026.6},
  annote =	{Keywords: ferry cover, river crossing, block-cut tree, st-numbering, hereditary graph property, connectivity}
}
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.2026.89
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}
}
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.2026.103
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.2026.53
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.2026.34
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.2026.105
Fixed-Parameter Tractable Submodular Maximization over a Matroid

Authors: Shamisa Nematollahi, Adrian Vladu, and Junyao Zhao

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

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

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

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@InProceedings{nematollahi_et_al:LIPIcs.ITCS.2026.105,
  author =	{Nematollahi, Shamisa and Vladu, Adrian and Zhao, Junyao},
  title =	{{Fixed-Parameter Tractable Submodular Maximization over a Matroid}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{105:1--105:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.105},
  URN =		{urn:nbn:de:0030-drops-253924},
  doi =		{10.4230/LIPIcs.ITCS.2026.105},
  annote =	{Keywords: Submodular maximization, matroids, parameterized complexity, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.19
Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

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

Abstract
Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].
Cite as

Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.IPEC.2025.19,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.19},
  URN =		{urn:nbn:de:0030-drops-251516},
  doi =		{10.4230/LIPIcs.IPEC.2025.19},
  annote =	{Keywords: Parameterized complexity, connected odd cycle transversal, clique-width}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.11
Courcelle’s Theorem for Lipschitz Continuity

Authors: Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida

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

Abstract
Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable decision-making and reproducible scientific research. Several studies have proposed Lipschitz continuous algorithms for various combinatorial optimization problems, but these algorithms are problem-specific, requiring a separate design for each problem. To address this issue, we provide the first algorithmic meta-theorem in the field of Lipschitz continuous algorithms. Our result can be seen as a Lipschitz continuous analogue of Courcelle’s theorem, which offers Lipschitz continuous algorithms for problems on bounded-treewidth graphs. Specifically, we consider the problem of finding a vertex set in a graph that maximizes or minimizes the total weight, subject to constraints expressed in monadic second-order logic (MSO₂). We show that for any ε > 0, there exists a (1±ε)-approximation algorithm for the problem with a polylogarithmic Lipschitz constant on bounded treewidth graphs. On such graphs, our result outperforms most existing Lipschitz continuous algorithms in terms of approximability and/or Lipschitz continuity. Further, we provide similar results for problems on bounded-clique-width graphs subject to constraints expressed in MSO₁. Additionally, we construct a Lipschitz continuous version of Baker’s decomposition using our meta-theorem as a subroutine.
Cite as

Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida. Courcelle’s Theorem for Lipschitz Continuity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.ESA.2025.11,
  author =	{Gima, Tatsuya and Kumabe, Soh and Yoshida, Yuichi},
  title =	{{Courcelle’s Theorem for Lipschitz Continuity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.11},
  URN =		{urn:nbn:de:0030-drops-244793},
  doi =		{10.4230/LIPIcs.ESA.2025.11},
  annote =	{Keywords: Fixed-Parameter Tractability, Algorithmic Meta-Theorem, Lipschitz Continuity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.78
Testing Depth First Search Numbering

Authors: Artur Czumaj, Christian Sohler, and Stefan Walzer

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

Abstract
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with sublinear query complexity. Here, a graph property P is testable with a sublinear query complexity if there is an algorithm that makes a sublinear number of queries to the input graph and accepts with probability at least 2/3, if the graph has property P, and rejects with probability at least 2/3 if it is ε-far from every graph that has property P. In this paper, we introduce a new variant of the bounded degree graph model. In this variant, in addition to the standard representation of a bounded degree graph, we assume that every vertex v has a unique label num(v) from {1, … , |V|}, and in addition to the standard queries in the bounded degree graph model, we also allow a property testing algorithm to query for the label of a vertex (but not for a vertex with a given label). Our new model is motivated by certain graph processes such as a DFS traversal, which assign consecutive numbers (labels) to the vertices of the graph. We want to study which of these numberings can be tested in sublinear time. As a first step in understanding such a model, we develop a property testing algorithm for discovery times of a DFS traversal with query complexity O(n^{1/3}/ε) and for constant ε > 0 we give a matching lower bound.
Cite as

Artur Czumaj, Christian Sohler, and Stefan Walzer. Testing Depth First Search Numbering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 78:1-78:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czumaj_et_al:LIPIcs.ESA.2025.78,
  author =	{Czumaj, Artur and Sohler, Christian and Walzer, Stefan},
  title =	{{Testing Depth First Search Numbering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{78:1--78:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.78},
  URN =		{urn:nbn:de:0030-drops-245466},
  doi =		{10.4230/LIPIcs.ESA.2025.78},
  annote =	{Keywords: Randomized Algorithms, Graph Algorithms, Property Testing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.77
Tolerant Testers for Subgraph-Freeness

Authors: Reut Levi and Jonathan Meiri

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

Abstract
In this paper we study the problem of tolerantly testing the property of being H-free (which also implies distance approximation from being H-free). In the general-graphs model, we show that for tolerant K_k-freeness testing can be achieved with query complexity that is polynomial in the arboricity of the input graph G, arb(G), and independent of the size of G (for graphs in which the average degree is Ω(1)). Specifically for triangles, our algorithm distinguished graphs which are ε-close to being triangle-free from graphs that 3ε(1+η)-far from being triangle-free with expected query complexity which is Õ(arb³(G)) (for constant η and ε). For general k-cliques our algorithm distinguishes graphs which are ε-close to being K_k-free from graphs which are binom(k,2)ε(1+η)-far from being K_k-free with expected query complexity which is polynomial in k, ε, γ and arb(G). We then generalize our result and provide a similar result for any motif H which is 2-connected of radius 1. This includes for example the wheel-graph. Finally, we show that our tester can be applied to the bounded-degree model for tolerantly testing H-freeness for any motif H. The query complexity of the algorithm is polynomial in the degree bound, d, improving the previous state-of-the-art by Marko and Ron (TALG 2009) that obtained quasi-polynomial query complexity in d.
Cite as

Reut Levi and Jonathan Meiri. Tolerant Testers for Subgraph-Freeness. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 77:1-77:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{levi_et_al:LIPIcs.ESA.2025.77,
  author =	{Levi, Reut and Meiri, Jonathan},
  title =	{{Tolerant Testers for Subgraph-Freeness}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{77:1--77:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.77},
  URN =		{urn:nbn:de:0030-drops-245456},
  doi =		{10.4230/LIPIcs.ESA.2025.77},
  annote =	{Keywords: Tolerant Testing, Property Testing, Subgraph freeness, distance approximation, arboricity}
}
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