10 Search Results for "Miyamoto, Masayuki"

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.2025.18
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.CCC.2025.17
Space-Bounded Quantum Interactive Proof Systems

Authors: François Le Gall, Yupan Liu, Harumichi Nishimura, and Qisheng Wang

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

Abstract
We introduce two models of space-bounded quantum interactive proof systems, QIPL and QIP_{U}L. The QIP_{U}L model, a space-bounded variant of quantum interactive proofs (QIP) introduced by Watrous (CC 2003) and Kitaev and Watrous (STOC 2000), restricts verifier actions to unitary circuits. In contrast, QIPL allows logarithmically many pinching intermediate measurements per verifier action, making it the weakest model that encompasses the classical model of Condon and Ladner (JCSS 1995). We characterize the computational power of QIPL and QIP_{U}L. When the message number m is polynomially bounded, QIP_{U}L ⊊ QIPL unless P = NP: - QIPL^HC, a subclass of QIPL defined by a high-concentration condition on yes instances, exactly characterizes NP. - QIP_{U}L is contained in P and contains SAC¹ ∪ BQL, where SAC¹ denotes problems solvable by classical logarithmic-depth, semi-unbounded fan-in circuits. However, this distinction vanishes when m is constant. Our results further indicate that (pinching) intermediate measurements uniquely impact space-bounded quantum interactive proofs, unlike in space-bounded quantum computation, where BQL = BQ_{U}L. We also introduce space-bounded unitary quantum statistical zero-knowledge (QSZK_{U}L), a specific form of QIP_{U}L proof systems with statistical zero-knowledge against any verifier. This class is a space-bounded variant of quantum statistical zero-knowledge (QSZK) defined by Watrous (SICOMP 2009). We prove that QSZK_{U}L = BQL, implying that the statistical zero-knowledge property negates the computational advantage typically gained from the interaction.
Cite as

François Le Gall, Yupan Liu, Harumichi Nishimura, and Qisheng Wang. Space-Bounded Quantum Interactive Proof Systems. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{legall_et_al:LIPIcs.CCC.2025.17,
  author =	{Le Gall, Fran\c{c}ois and Liu, Yupan and Nishimura, Harumichi and Wang, Qisheng},
  title =	{{Space-Bounded Quantum Interactive Proof Systems}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.17},
  URN =		{urn:nbn:de:0030-drops-237115},
  doi =		{10.4230/LIPIcs.CCC.2025.17},
  annote =	{Keywords: Intermediate measurements, Quantum interactive proofs, Space-bounded quantum computation}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.34
Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries

Authors: François Le Gall, Oran Nadler, Harumichi Nishimura, and Rotem Oshman

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
In this paper we study a quantum version of the multiparty simultaneous message-passing (SMP) model, and we show that in some cases, quantum communication can replace public randomness, even with no entanglement between the parties. This was already known for two players, but not for more than two players, and indeed, so far all that was known was a negative result. Our main technical contribution is a compiler that takes any classical public-coin simultaneous protocol based on "modified equality queries," and converts it into a quantum simultaneous protocol without public coins with roughly the same communication complexity. We then use our compiler to derive protocols for several problems, including frequency moments, neighborhood diversity, enumeration of isolated cliques, and more.
Cite as

François Le Gall, Oran Nadler, Harumichi Nishimura, and Rotem Oshman. Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{legall_et_al:LIPIcs.OPODIS.2024.34,
  author =	{Le Gall, Fran\c{c}ois and Nadler, Oran and Nishimura, Harumichi and Oshman, Rotem},
  title =	{{Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.34},
  URN =		{urn:nbn:de:0030-drops-225701},
  doi =		{10.4230/LIPIcs.OPODIS.2024.34},
  annote =	{Keywords: SMP model, multi-party communication, quantum distributed algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.63
Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [QIP 2023] under the term state synthesis. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state U|ψ⟩ at the rightmost node of the line, where |ψ⟩ is a quantum state given at the leftmost node and U is a unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.
Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{legall_et_al:LIPIcs.MFCS.2023.63,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{63:1--63:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.63},
  URN =		{urn:nbn:de:0030-drops-185975},
  doi =		{10.4230/LIPIcs.MFCS.2023.63},
  annote =	{Keywords: distributed quantum Merlin-Arthur, distributed verification, quantum computation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.42
Distributed Quantum Interactive Proofs

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs. In this paper, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The first result of this paper shows that by using distributed quantum interactive proofs, the number of interactions can be significantly reduced. More precisely, our result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to three. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well. As a corollary of our results, we show that there exist 5-turn/3-turn distributed quantum interactive protocols with small certificate size for problems that have been considered in prior works on distributed interactive proofs such as [Kol, Oshman, and Saxena PODC 2018, Naor, Parter, and Yogev SODA 2020]. We then utilize the framework of the distributed quantum interactive proofs to test closeness of two quantum states each of which is distributed over the entire network.
Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Distributed Quantum Interactive Proofs. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{legall_et_al:LIPIcs.STACS.2023.42,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Distributed Quantum Interactive Proofs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{42:1--42:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.42},
  URN =		{urn:nbn:de:0030-drops-176949},
  doi =		{10.4230/LIPIcs.STACS.2023.42},
  annote =	{Keywords: distributed interactive proofs, distributed verification, quantum computation}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.48
Brief Announcement: Distributed Quantum Interactive Proofs

Authors: François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs. In this brief announcement, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The main result of this paper shows that by using quantum distributed interactive proofs, the number of interactions can be significantly reduced. More precisely, our main result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to 3-turn. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well.
Cite as

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Brief Announcement: Distributed Quantum Interactive Proofs. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{legall_et_al:LIPIcs.DISC.2022.48,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki and Nishimura, Harumichi},
  title =	{{Brief Announcement: Distributed Quantum Interactive Proofs}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{48:1--48:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.48},
  URN =		{urn:nbn:de:0030-drops-172396},
  doi =		{10.4230/LIPIcs.DISC.2022.48},
  annote =	{Keywords: distributed interactive proofs, distributed verification, quantum computation}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.15
Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

Authors: Amir Nikabadi and Janne H. Korhonen

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems.
Cite as

Amir Nikabadi and Janne H. Korhonen. Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nikabadi_et_al:LIPIcs.OPODIS.2021.15,
  author =	{Nikabadi, Amir and Korhonen, Janne H.},
  title =	{{Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.15},
  URN =		{urn:nbn:de:0030-drops-157902},
  doi =		{10.4230/LIPIcs.OPODIS.2021.15},
  annote =	{Keywords: distributed algorithms, parameterized distributed complexity, CONGEST model, induced subgraph detection, graph parameters, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.58
Lower Bounds for Induced Cycle Detection in Distributed Computing

Authors: François Le Gall and Masayuki Miyamoto

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
The distributed subgraph detection asks, for a fixed graph H, whether the n-node input graph contains H as a subgraph or not. In the standard CONGEST model of distributed computing, the complexity of clique/cycle detection and listing has received a lot of attention recently. In this paper we consider the induced variant of subgraph detection, where the goal is to decide whether the n-node input graph contains H as an induced subgraph or not. We first show a Ω̃(n) lower bound for detecting the existence of an induced k-cycle for any k ≥ 4 in the CONGEST model. This lower bound is tight for k = 4, and shows that the induced variant of k-cycle detection is much harder than the non-induced version. This lower bound is proved via a reduction from two-party communication complexity. We complement this result by showing that for 5 ≤ k ≤ 7, this Ω̃(n) lower bound cannot be improved via the two-party communication framework. We then show how to prove stronger lower bounds for larger values of k. More precisely, we show that detecting an induced k-cycle for any k ≥ 8 requires Ω̃(n^{2-Θ{(1/k)}}) rounds in the CONGEST model, nearly matching the known upper bound Õ(n^{2-Θ{(1/k)}}) of the general k-node subgraph detection (which also applies to the induced version) by Eden, Fiat, Fischer, Kuhn, and Oshman [DISC 2019]. Finally, we investigate the case where H is the diamond (the diamond is obtained by adding an edge to a 4-cycle, or equivalently removing an edge from a 4-clique), and show non-trivial upper and lower bounds on the complexity of the induced version of diamond detecting and listing.
Cite as

François Le Gall and Masayuki Miyamoto. Lower Bounds for Induced Cycle Detection in Distributed Computing. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 58:1-58:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{legall_et_al:LIPIcs.ISAAC.2021.58,
  author =	{Le Gall, Fran\c{c}ois and Miyamoto, Masayuki},
  title =	{{Lower Bounds for Induced Cycle Detection in Distributed Computing}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{58:1--58:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.58},
  URN =		{urn:nbn:de:0030-drops-154919},
  doi =		{10.4230/LIPIcs.ISAAC.2021.58},
  annote =	{Keywords: Distributed computing, Lower bounds, Subgraph detection}
}
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