70 Search Results for "Le Gall, Francois"

Volume

LIPIcs, Volume 232

17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)

TQC 2022, July 11-15, 2022, Urbana Champaign, Illinois, USA

Editors: François Le Gall and Tomoyuki Morimae

Document
DOI: 10.4230/LIPIcs.CCC.2026.12
Fine-Grained Complexity for Quantum Problems from Size-Preserving Circuit-To-Hamiltonian Constructions

Authors: Nai-Hui Chia, Atsuya Hasegawa, François Le Gall, and Yu-Ching Shen

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
The local Hamiltonian (LH) problem is the canonical QMA-complete problem introduced by Kitaev. In this paper, we show its hardness in a very strong sense: we show that the 3-local Hamiltonian problem on n qubits cannot be solved classically in time O(2^{(1-ε)n}) for any ε > 0 under the Strong Exponential-Time Hypothesis (SETH), and cannot be solved quantumly in time O(2^{(1-ε)n/2}) for any ε > 0 under the Quantum Strong Exponential-Time Hypothesis (QSETH). These lower bounds give evidence that the currently known classical and quantum algorithms for LH cannot be significantly improved. Furthermore, we are able to demonstrate fine-grained complexity lower bounds for approximating the quantum partition function (QPF) with an arbitrary constant relative error. Approximating QPF with relative error is known to be equivalent to approximately counting the dimension of the solution subspace of QMA problems. We show the SETH and QSETH hardness to estimate QPF with constant relative error. We then provide a quantum algorithm that runs in O(√{2ⁿ}) time for an arbitrary 1/poly(n) relative error, matching our lower bounds and improving the state-of-the-art algorithm by Bravyi, Chowdhury, Gosset, and Wocjan (Nature Physics 2022) in the low-temperature regime. To prove our fine-grained lower bounds, we introduce the first size-preserving circuit-to-Hamiltonian construction that encodes the computation of a T-time quantum circuit acting on N qubits into a (d+1)-local Hamiltonian acting on N+O(T^{1/d}) qubits. This improves the standard construction based on the unary clock, which uses N+O(T) qubits.
Cite as

Nai-Hui Chia, Atsuya Hasegawa, François Le Gall, and Yu-Ching Shen. Fine-Grained Complexity for Quantum Problems from Size-Preserving Circuit-To-Hamiltonian Constructions. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 12:1-12:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chia_et_al:LIPIcs.CCC.2026.12,
  author =	{Chia, Nai-Hui and Hasegawa, Atsuya and Le Gall, Fran\c{c}ois and Shen, Yu-Ching},
  title =	{{Fine-Grained Complexity for Quantum Problems from Size-Preserving Circuit-To-Hamiltonian Constructions}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{12:1--12:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.12},
  URN =		{urn:nbn:de:0030-drops-270543},
  doi =		{10.4230/LIPIcs.CCC.2026.12},
  annote =	{Keywords: Fine-grain complexity, SETH, QSETH, Local Hamiltonian problem, Quantum partition problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.97
Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding

Authors: Amin Shiraz Gilani, Daochen Wang, Pei Wu, and Xingyu Zhou

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks whether there exists a triangle containing a target edge and raises general questions about the hiding of a problem’s input among irrelevant data. The second asks whether there exists a triangle containing a target vertex and raises general questions about the shuffling of a problem’s input. The third asks whether there exists a triangle; this problem bridges the 3-distinctness and 3-sum problems, which have been extensively studied by both cryptographers and complexity theorists. We provide tight or nearly tight results for these problems as well as some first answers to the general questions they raise. Furthermore, given any graph with low maximum degree, such as a typical random sparse graph, we prove that the quantum query complexity of finding a length-k cycle in its length-m edge list is m^{3/4-1/(2^{k+2}-4) ± o(1)}, which matches the best-known upper bound for the quantum query complexity of k-distinctness on length-m inputs up to an m^o(1) factor. We prove the lower bound by developing new techniques within Zhandry’s recording query framework [Zhandry, 2019] as generalized by Hamoudi and Magniez [Hamoudi and Magniez, 2023]. These techniques extend the framework to treat any non-product distribution that results from conditioning a product distribution on the absence of rare events. We prove the upper bound by adapting Belovs’s learning graph algorithm for k-distinctness [Belovs, 2012]. Finally, assuming a plausible conjecture concerning only cycle finding, we show that the lower bound can be lifted to an essentially tight lower bound on the quantum query complexity of k-distinctness, which is a long-standing open question.
Cite as

Amin Shiraz Gilani, Daochen Wang, Pei Wu, and Xingyu Zhou. Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 97:1-97:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gilani_et_al:LIPIcs.ICALP.2026.97,
  author =	{Gilani, Amin Shiraz and Wang, Daochen and Wu, Pei and Zhou, Xingyu},
  title =	{{Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{97:1--97:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.97},
  URN =		{urn:nbn:de:0030-drops-264867},
  doi =		{10.4230/LIPIcs.ICALP.2026.97},
  annote =	{Keywords: Quantum query complexity, graph algorithms, edge list model}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.30
Parallel Algorithms for Group Isomorphism via Code Equivalence

Authors: Michael Levet

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

Abstract
In this paper, we exhibit AC³ isomorphism tests for coprime extensions H ⋉ N where H is elementary Abelian and N is Abelian; and groups where Rad(G) = Z(G) is elementary Abelian and G = Soc^{*}(G). The fact that isomorphism testing for these families is in P was established respectively by Qiao, Sarma, and Tang (STACS 2011), and Grochow and Qiao (CCC 2014, SIAM J. Comput. 2017). The polynomial-time isomorphism tests for both of these families crucially leveraged small (size O(log |G|)) instances of Linear Code Equivalence (Babai, SODA 2011). Here, we combine Luks' group-theoretic method for Graph Isomorphism (FOCS 1980, J. Comput. Syst. Sci. 1982) with the fact that G is given by its multiplication table, to implement the corresponding instances of Linear Code Equivalence in AC³. As a byproduct of our work, we show that isomorphism testing of arbitrary central-radical groups is decidable using AC circuits of depth O(log³ n) and size n^{O(log log n)}. This improves upon the previous bound of n^{O(log log n)}-time due to Grochow and Qiao (ibid.).
Cite as

Michael Levet. Parallel Algorithms for Group Isomorphism via Code Equivalence. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levet:LIPIcs.SWAT.2026.30,
  author =	{Levet, Michael},
  title =	{{Parallel Algorithms for Group Isomorphism via Code Equivalence}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{30:1--30:19},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-260660},
  doi =		{10.4230/LIPIcs.SWAT.2026.30},
  annote =	{Keywords: Group Isomorphism, Circuit Complexity, Code Equivalence}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.66
Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

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

Abstract
We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.
Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}
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.2026.108
The Learning Stabilizers with Noise Problem

Authors: Alexander Poremba, Yihui Quek, and Peter Shor

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

Abstract
Random classical codes have good error correcting properties, and yet they are notoriously hard to decode in practice. Despite many decades of extensive study, the fastest known algorithms still run in exponential time. The Learning Parity with Noise (LPN) problem, which can be seen as the task of decoding a random linear code in the presence of noise, has thus emerged as a prominent hardness assumption with numerous applications in both cryptography and learning theory. Is there a natural quantum analog of the LPN problem? In this work, we introduce the Learning Stabilizers with Noise (LSN) problem, the task of decoding a random stabilizer code in the presence of local depolarizing noise. We give both polynomial-time and exponential-time quantum algorithms for solving LSN in various depolarizing noise regimes, ranging from extremely low noise, to low constant noise rates, and even higher noise rates up to a threshold. Next, we provide concrete evidence that LSN is hard. First, we show that LSN includes LPN as a special case, which suggests that it is at least as hard as its classical counterpart. Second, we prove worst-case to average-case reductions for variants of LSN. We then ask: what is the computational complexity of solving LSN? Because the task features quantum inputs, its complexity cannot be characterized by traditional complexity classes. Instead, we show that the LSN problem lies in a recently introduced (distributional and oracle) unitary synthesis class. Finally, we identify several applications of our LSN assumption, ranging from the construction of quantum bit commitment schemes to the computational limitations of learning from quantum data.
Cite as

Alexander Poremba, Yihui Quek, and Peter Shor. The Learning Stabilizers with Noise Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 108:1-108:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{poremba_et_al:LIPIcs.ITCS.2026.108,
  author =	{Poremba, Alexander and Quek, Yihui and Shor, Peter},
  title =	{{The Learning Stabilizers with Noise Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{108:1--108:19},
  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.2026.108},
  URN =		{urn:nbn:de:0030-drops-253950},
  doi =		{10.4230/LIPIcs.ITCS.2026.108},
  annote =	{Keywords: Random quantum stabilizer codes, average-case hardness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.73
Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals

Authors: Daniel Grier, Daniel M. Kane, Jackson Morris, Anthony Ostuni, and Kewen Wu

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

Abstract
We construct a family of distributions {𝒟_n}_n with 𝒟_n over {0, 1}ⁿ and a family of depth-7 quantum circuits {C_n}_n such that 𝒟_n is produced exactly by C_n with the all zeros state as input, yet any constant-depth classical circuit with bounded fan-in gates evaluated on any binary product distribution has total variation distance 1 - e^{-Ω(n)} from 𝒟_n. Moreover, the quantum circuits we construct are geometrically local and use a relatively standard gate set: Hadamard, controlled-phase, CNOT, and Toffoli gates. All previous separations of this type suffer from some undesirable constraint on the classical circuit model or the quantum circuits witnessing the separation. Our family of distributions is inspired by the Parity Halving Problem of Watts, Kothari, Schaeffer, and Tal (STOC, 2019), which built on the work of Bravyi, Gosset, and König (Science, 2018) to separate shallow quantum and classical circuits for relational problems.
Cite as

Daniel Grier, Daniel M. Kane, Jackson Morris, Anthony Ostuni, and Kewen Wu. Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grier_et_al:LIPIcs.ITCS.2026.73,
  author =	{Grier, Daniel and Kane, Daniel M. and Morris, Jackson and Ostuni, Anthony and Wu, Kewen},
  title =	{{Quantum Advantage from Sampling Shallow Circuits: Beyond Hardness of Marginals}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{73:1--73:14},
  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.2026.73},
  URN =		{urn:nbn:de:0030-drops-253607},
  doi =		{10.4230/LIPIcs.ITCS.2026.73},
  annote =	{Keywords: Shallow circuits, sampling, quantum circuits}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.10
Computing in a Faulty Congested Clique

Authors: Keren Censor-Hillel and Pedro Soto

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of O(nlog{n})-bit input per node can be solved in roughly n rounds, where n is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm 𝒜 for the non-faulty Congested Clique model, we show how to transform it into an algorithm 𝒜' for the faulty model, with an overhead that could be as small as some logarithmic-in-n factor, by considering refined complexity measures of 𝒜. As an exemplifying application of our approach, we show that the O(n^{1/3})-round complexity of semi-ring matrix multiplication [Censor{-}Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail 99% of the nodes (or any other constant fraction).
Cite as

Keren Censor-Hillel and Pedro Soto. Computing in a Faulty Congested Clique. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2025.10,
  author =	{Censor-Hillel, Keren and Soto, Pedro},
  title =	{{Computing in a Faulty Congested Clique}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.10},
  URN =		{urn:nbn:de:0030-drops-251833},
  doi =		{10.4230/LIPIcs.OPODIS.2025.10},
  annote =	{Keywords: distributed computing, graph algorithms, computing with faults}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.19
Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL

Authors: Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an advantage over SLOCAL is 3-coloring bipartite graphs. Recently, Chang et al. [PODC 2024] showed that even in grids, 3-coloring requires Ω(log n) locality in deterministic online-LOCAL. This result was subsequently extended by Akbari et al. [STOC 2025] to also hold in randomized online-LOCAL. However, both proofs heavily rely on the assumption that the algorithm does not have access to the orientation of the underlying grid. In this paper, we show how to lift this requirement and obtain the same lower bound (against either model) even when the algorithm is explicitly given a globally consistent orientation of the grid.
Cite as

Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert. Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boudier_et_al:LIPIcs.OPODIS.2025.19,
  author =	{Boudier, Thomas and Casagrande, Filippo and Das, Avinandan and Equi, Massimo and Lievonen, Henrik and Modanese, Augusto and Stimpert, Ronja},
  title =	{{Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251925},
  doi =		{10.4230/LIPIcs.OPODIS.2025.19},
  annote =	{Keywords: coloring, locally checkable labeling problems, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.51
Distributed Complexity of P_k-Freeness: Decision and Certification

Authors: Masayuki Miyamoto

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The class of graphs that do not contain a path on k nodes as an induced subgraph (P_k-free graphs) has rich applications in the theory of graph algorithms. This paper explores the problem of deciding P_k-freeness from the viewpoint of distributed computing. For specific small values of k, we present the first CONGEST algorithms specified for P_k-freeness, utilizing structural properties of P_k-free graphs in a novel way. Specifically, we show that P_k-freeness can be decided in Õ(1) rounds for k = 4 in the broadcast CONGEST model, and in Õ(n) rounds for k = 5 in the CONGEST model, where n is the number of nodes in the network and Õ(⋅) hides a polylog(n) factor. The main technical contribution is a novel technique used in our algorithm for P₅-freeness to distinguish induced 5-paths from non-induced ones, which is potentially applicable to other induced subgraphs. This technique also enables the construction of a local certification of P₅-freeness with certificates of size Õ(n). This improves Õ(n^{3/2}) by Bousquet and Zeitoun (TCS 2025), and is nearly optimal, given our Ω(n^{1-o(1)}) lower bound on certificate size. For general k, we establish the first CONGEST lower bound, which is of the form n^{2-1/Θ(k)}. The n^{1/Θ(k)} factor is unavoidable, in view of the O(n^{2-2/(3k+2)}) upper bound by Eden et al. (Dist. Comp. 2022). Additionally, our approach yields the first superlinear lower bound on certificate size for local certification. This partially answers the conjecture on the optimal certificate size of P_k-freeness, asked by Bousquet et al. (arXiv:2402.12148). Finally, we propose a novel variant of the problem called ordered P_k detection. We show that in the CONGEST model, the round complexity of ordered P_k detection is Ω̃(n) for k ≥ 5, and in contrast, proving any nontrivial lower bound for ordered P₃ detection implies a strong circuit lower bound. As a byproduct, we establish a circuit-complexity barrier for Ω(n^{1/2+ε}) quantum CONGEST lower bounds for induced 4-cycle detection. This is complemented by our Õ(n^{3/4}) quantum upper bound, which surpasses the classical Ω̃(n) lower bound by Le Gall and Miyamoto (ISAAC 2021).
Cite as

Masayuki Miyamoto. Distributed Complexity of P_k-Freeness: Decision and Certification. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{miyamoto:LIPIcs.ISAAC.2025.51,
  author =	{Miyamoto, Masayuki},
  title =	{{Distributed Complexity of P\underlinek-Freeness: Decision and Certification}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.51},
  URN =		{urn:nbn:de:0030-drops-249597},
  doi =		{10.4230/LIPIcs.ISAAC.2025.51},
  annote =	{Keywords: subgraph detection, CONGEST model, local certification}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.34
New Distributed Interactive Proofs for Planarity: A Matter of Left and Right

Authors: Yuval Gil and Merav Parter

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

Abstract
We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a distributed interactive proof (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier consists of n nodes connected by a communication graph G. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph G satisfies a certain property (e.g., planarity) in a small number of rounds, and with a small communication bound, denoted as the proof size. Prior work by Naor, Parter and Yogev (SODA 2020) presented a DIP for planarity that uses three interaction rounds and a proof size of O(log n). Feuilloley et al. (PODC 2020) showed that the same can be achieved with a single interaction round and without randomization, by providing a proof labeling scheme with a proof size of O(log n). In a subsequent work, Bousquet, Feuilloley, and Pierron (OPODIS 2021) achieved the same bound for related graph families such as outerplanarity, series-parallel graphs, and graphs of treewidth at most 2. In this work, we design new DIPs that use exponentially shorter proofs compared to the state-of-the-art bounds. Our main results are: - There is a 5-round protocol with O(log log n) proof size for outerplanarity. - There is a 5-round protocol with O(log log n) proof size for verifying embedded planarity and O(log log n+log Δ) proof size for general planar graphs, where Δ is the maximum degree in the graph. In the former setting, it is assumed that an embedding of the graph is given (e.g., each node holds a clockwise orientation of its neighbors) and the goal is to verify that it is a valid planar embedding. The latter result should be compared with the non-interactive setting for which there is lower bound of Ω(log n) bits for graphs with Δ = O(1) by Feuilloley et al. (PODC 2020). - The non-interactive deterministic lower bound of Ω(log n) bits by Feuilloley et al. (PODC 2020) can be extended to hold even if the verifier is randomized. Moreover, the lower bound holds even with the assumption that the verifier’s randomness comes in the form of an unbounded random string shared among the nodes. We also show that our DIPs can be extended to protocols with similar bounds for verifying series-parallel graphs and graphs with tree-width at most 2. Perhaps surprisingly, our results demonstrate that the key technical barrier for obtaining o(log log n) labels for all our problems is a basic sorting verification task in which all nodes are embedded on an oriented path P ⊆ G and it is desired for each node to distinguish between its left and right G-neighbors.
Cite as

Yuval Gil and Merav Parter. New Distributed Interactive Proofs for Planarity: A Matter of Left and Right. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 34:1-34:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gil_et_al:LIPIcs.DISC.2025.34,
  author =	{Gil, Yuval and Parter, Merav},
  title =	{{New Distributed Interactive Proofs for Planarity: A Matter of Left and Right}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{34:1--34:23},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-248515},
  doi =		{10.4230/LIPIcs.DISC.2025.34},
  annote =	{Keywords: Distributed interactive proofs, Planar graphs}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.22
The Complexity Landscape of Dynamic Distributed Subgraph Finding

Authors: Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang

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

Abstract
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques in the deterministic setting. For finding cliques, we establish an Ω(log log n) bandwidth lower bound for one-round membership-detection under edge insertions only and an Ω(log log log n) bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems. For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.
Cite as

Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang. The Complexity Landscape of Dynamic Distributed Subgraph Finding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chang_et_al:LIPIcs.DISC.2025.22,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Chen, Yanyu and Mishra, Gopinath and Yang, Mingyang},
  title =	{{The Complexity Landscape of Dynamic Distributed Subgraph Finding}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{22:1--22:20},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-248399},
  doi =		{10.4230/LIPIcs.DISC.2025.22},
  annote =	{Keywords: Distributed algorithms, dynamic algorithms, subgraph finding}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.20
Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique

Authors: Keren Censor-Hillel, Orr Fischer, Ran Gelles, and Pedro Soto

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

Abstract
We design a deterministic compiler that makes any computation in the Congested Clique model robust to a constant fraction α < 1 of adversarial crash faults. In particular, we show how a network of n nodes can compute any circuit of depth d, width ω, and gate total fan Δ, in d ⋅ ⌈ω/n² + Δ/n⌉ ⋅ 2^{O(√{log{n}}log log{n})} rounds in such a faulty model. As a corollary, any T-round Congested Clique algorithm can be compiled into an algorithm that completes in T² n^{o(1)} rounds in this model. Our compiler obtains resilience to node crashes by coding information across the network, and its main underlying observation is that we can leverage locally-decodable codes (LDCs) to maintain a low complexity overhead, as these allow recovering the information needed at each computational step by querying only small parts of the codeword, instead of retrieving the entire coded message, which is inherent when using block codes. The main technical contribution is that because erasures occur in known locations, which correspond to crashed nodes, we can derandomize classical LDC constructions by deterministically selecting query sets that avoid sufficiently many erasures. Moreover, when decoding multiple codewords in parallel, our derandomization load-balances the queries per-node, thereby preventing congestion and maintaining a low round complexity. Deterministic decoding of LDCs presents a new challenge: the adversary can target precisely the (few) nodes that are queried for decoding a certain codeword. We overcome this issue via an adaptive doubling strategy: if a decoding attempt for a codeword fails, the node doubles the number of its decoding attempts. We employ a similar doubling technique when the adversary crashes the decoding node itself, replacing it dynamically with two other non-crashed nodes. By carefully combining these two doubling processes, we overcome the challenges posed by the combination of a deterministic LDC with a worst case pattern of crashes.
Cite as

Keren Censor-Hillel, Orr Fischer, Ran Gelles, and Pedro Soto. Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.DISC.2025.20,
  author =	{Censor-Hillel, Keren and Fischer, Orr and Gelles, Ran and Soto, Pedro},
  title =	{{Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{20:1--20:19},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-248379},
  doi =		{10.4230/LIPIcs.DISC.2025.20},
  annote =	{Keywords: Congested Clique, Fault Tolerance, Error Correction Codes}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.11
New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs

Authors: Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco d'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela

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

Abstract
In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing: 1) We show that there is no distributed quantum advantage for any linear program. Put otherwise, if there is a quantum-LOCAL algorithm 𝒜 that finds an α-approximation of some linear optimization problem Π in T communication rounds, we can construct a classical, deterministic LOCAL algorithm 𝒜' that finds an α-approximation of Π in T rounds. As a corollary, all classical lower bounds for linear programs, including the KMW bound, hold verbatim in quantum-LOCAL. 2) Using the above result, we show that there exists a locally checkable labeling problem (LCL) for which quantum-LOCAL is strictly weaker than the classical deterministic SLOCAL model. Our results extend from quantum-LOCAL to finitely dependent and non-signaling distributions, and one of the corollaries of our work is that the non-signaling model and the SLOCAL model are incomparable in the context of LCL problems: By prior work, there exists an LCL problem for which SLOCAL is strictly weaker than the non-signaling model, and our work provides a separation in the opposite direction.
Cite as

Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco d'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela. New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.11,
  author =	{Balliu, Alkida and Coupette, Corinna and Cruciani, Antonio and d'Amore, Francesco and Equi, Massimo and Lievonen, Henrik and Modanese, Augusto and Olivetti, Dennis and Suomela, Jukka},
  title =	{{New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{11:1--11:22},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-248280},
  doi =		{10.4230/LIPIcs.DISC.2025.11},
  annote =	{Keywords: linear programming, distributed quantum advantage, quantum-LOCAL model, SLOCAL model, online-LOCAL model, non-signaling distributions, locally checkable labeling problems, dequantization}
}
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