10 Search Results for "Kitamura, Naoki"

Document
DOI: 10.4230/LIPIcs.OPODIS.2025.34
Uniform Deployment of Mobile Robots in Complete Bipartite Graphs

Authors: Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, Yonghwan Kim, Yoshiaki Katayama, Toshimitsu Masuzawa, Quentin Bramas, and Sébastien Tixeuil

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

Abstract
In this paper, we address the problem of uniformly deploying mobile robots in complete bipartite graphs. Specifically, when n robots are positioned arbitrarily at distinct nodes in a complete bipartite graph K_{n,n}, which consists of two n-node sets V_L and V_R, the uniform deployment problem requires the robots to achieve one of the following configurations: (a) each node in V_L is occupied by exactly one robot, with no robots in V_R, or (b) each node in V_R is occupied by exactly one robot, with no robots in V_L. In either configuration, the distance between any two robots is 2, ensuring that the robots are uniformly deployed. In this paper, we explore the relationship between the visibility range of robots and the solvability of the uniform deployment problem. First, we characterize solvable and unsolvable initial configurations under the assumption that robots have an infinite visibility range. Next, we demonstrate that visibility range 1 (meaning robots can only observe nodes at a distance of 1 and the robots positioned on them) is insufficient, proving the impossibility of solving the problem under this constraint. Conversely, we show that visibility range Θ(log n) is sufficient by presenting an algorithm that solves the uniform deployment problem in O(1) rounds, starting from any solvable initial configuration. Finally, we briefly introduce an example showing that robots with a constant visibility range (which is 3 in this example) cannot solve the problem in a native way.
Cite as

Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, Yonghwan Kim, Yoshiaki Katayama, Toshimitsu Masuzawa, Quentin Bramas, and Sébastien Tixeuil. Uniform Deployment of Mobile Robots in Complete Bipartite Graphs. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shibata_et_al:LIPIcs.OPODIS.2025.34,
  author =	{Shibata, Masahiro and Kitamura, Naoki and Eguchi, Ryota and Sudo, Yuichi and Nakamura, Junya and Kim, Yonghwan and Katayama, Yoshiaki and Masuzawa, Toshimitsu and Bramas, Quentin and Tixeuil, S\'{e}bastien},
  title =	{{Uniform Deployment of Mobile Robots in Complete Bipartite Graphs}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{34:1--34:17},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-252075},
  doi =		{10.4230/LIPIcs.OPODIS.2025.34},
  annote =	{Keywords: mobile robots, uniform deployment, complete bipartite graphs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.39
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

Authors: Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou

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

Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as

Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
  title =	{{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-249474},
  doi =		{10.4230/LIPIcs.ISAAC.2025.39},
  annote =	{Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.40
On the Randomized Locality of Matching Problems in Regular Graphs

Authors: Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang

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

Abstract
The main goal in distributed symmetry-breaking is to understand the locality of problems: the radius of the neighborhood that a node must explore to determine its part of a global solution. In this work, we study the locality of matching problems in the family of regular graphs, which is one of the main benchmarks for establishing lower bounds on the locality of symmetry-breaking problems, as well as for obtaining classification results. Our main results are summarized as follows: 1) Approximate matching: We develop randomized algorithms to show that (1 + ε)-approximate matching in regular graphs is truly local, i.e., the locality depends only on ε and is independent of all other graph parameters. Furthermore, as long as the degree Δ is not very small (namely, as long as Δ ≥ poly(1/ε)), this dependence is only logarithmic in 1/ε. This stands in sharp contrast to maximal matching in regular graphs which requires some dependence on the number of nodes n or the degree Δ. 2) Maximal matching: Our techniques further allow us to establish a strong separation between the node-averaged complexity and worst-case complexity of maximal matching in regular graphs, by showing that the former is only O(1). Central to our main technical contribution is a novel martingale-based analysis for the ≈ 40-year-old algorithm by Luby. In particular, our analysis shows that applying one round of Luby’s algorithm on the line graph of a Δ-regular graph results in an almost Δ/2-regular graph.
Cite as

Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang. On the Randomized Locality of Matching Problems in Regular Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoury_et_al:LIPIcs.DISC.2025.40,
  author =	{Khoury, Seri and Purohit, Manish and Schild, Aaron and Wang, Joshua R.},
  title =	{{On the Randomized Locality of Matching Problems in Regular Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{40:1--40:20},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-248570},
  doi =		{10.4230/LIPIcs.DISC.2025.40},
  annote =	{Keywords: regular graphs, maximum matching, augmenting paths, distributed algorithms, Luby’s algorithm, martingales}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.45
Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs

Authors: Jinfeng Dou, Thorsten Götte, Henning Hillebrandt, Christian Scheideler, and Julian Werthmann

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We consider the distributed and parallel construction of low-diameter decompositions with strong diameter. We present algorithms for arbitrary undirected, weighted graphs and also for undirected, weighted graphs that can be separated through k ∈ Õ(1) shortest paths. This class of graphs includes planar graphs, graphs of bounded treewidth, and graphs that exclude a fixed minor K_r. Our algorithms work in the PRAM, CONGEST, and the novel HYBRID communication model and are competitive in all relevant parameters. Given 𝒟 > 0, our low-diameter decomposition algorithm divides the graph into connected clusters of strong diameter 𝒟. For an arbitrary graph, an edge e ∈ E of length 𝓁_e is cut between two clusters with probability O(𝓁_e⋅log(n)/𝒟). If the graph can be separated by k ∈ Õ(1) paths, the probability improves to O(𝓁_e⋅log(log n)/𝒟). In either case, the decompositions can be computed in Õ(1) depth and Õ(m) work in the PRAM and Õ(1) time in the HYBRID model. In CONGEST, the runtimes are Õ(HD + √n) and Õ(HD) respectively. All these results hold w.h.p. Broadly speaking, we present distributed and parallel implementations of sequential divide-and-conquer algorithms where we replace exact shortest paths with approximate shortest paths. In contrast to exact paths, these can be efficiently computed in the distributed and parallel setting [STOC '22]. Further, and perhaps more importantly, we show that instead of explicitly computing vertex-separators to enable efficient parallelization of these algorithms, it suffices to sample a few random paths of bounded length and the nodes close to them. Thereby, we do not require complex embeddings whose implementation is unknown in the distributed and parallel setting.
Cite as

Jinfeng Dou, Thorsten Götte, Henning Hillebrandt, Christian Scheideler, and Julian Werthmann. Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 45:1-45:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dou_et_al:LIPIcs.ITCS.2025.45,
  author =	{Dou, Jinfeng and G\"{o}tte, Thorsten and Hillebrandt, Henning and Scheideler, Christian and Werthmann, Julian},
  title =	{{Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{45:1--45:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.45},
  URN =		{urn:nbn:de:0030-drops-226734},
  doi =		{10.4230/LIPIcs.ITCS.2025.45},
  annote =	{Keywords: Distributed Graph Algorithms, Network Decomposition, Excluded Minor}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.12
Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings

Authors: Fukuhito Ooshita, Naoki Kitamura, Ryota Eguchi, Michiko Inoue, Hirotsugu Kakugawa, Sayaka Kamei, Masahiro Shibata, and Yuichi Sudo

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

Abstract
We investigate crash-tolerant perpetual exploration algorithms by myopic luminous robots on ring networks. Myopic robots mean that they can observe nodes only within a certain fixed distance ϕ, and luminous robots mean that they have light devices that can emit a color from a set of colors. The goal of perpetual exploration is to ensure that robots, starting from specific initial positions and colors, move in such a way that every node is visited by at least one robot infinitely often. As a main contribution, we clarify the tight necessary and sufficient number of robots to realize perpetual exploration when at most f robots crash. In the fully synchronous model, we prove that f+2 robots are necessary and sufficient for any ϕ ≥ 1. In the semi-synchronous and asynchronous models, we prove that 3f+3 (resp., 2f+2) robots are necessary and sufficient if ϕ = 1 (resp., ϕ ≥ 2).
Cite as

Fukuhito Ooshita, Naoki Kitamura, Ryota Eguchi, Michiko Inoue, Hirotsugu Kakugawa, Sayaka Kamei, Masahiro Shibata, and Yuichi Sudo. Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ooshita_et_al:LIPIcs.OPODIS.2024.12,
  author =	{Ooshita, Fukuhito and Kitamura, Naoki and Eguchi, Ryota and Inoue, Michiko and Kakugawa, Hirotsugu and Kamei, Sayaka and Shibata, Masahiro and Sudo, Yuichi},
  title =	{{Crash-Tolerant Perpetual Exploration with Myopic Luminous Robots on Rings}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{12:1--12:16},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-225486},
  doi =		{10.4230/LIPIcs.OPODIS.2024.12},
  annote =	{Keywords: mobile robots, crash faults, LCM model, exploration}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.65
A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles

Authors: Kaito Harada, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
An α-approximate vertex fault-tolerant distance sensitivity oracle (α-VSDO) for a weighted input graph G = (V, E, w) and a source vertex s ∈ V is the data structure answering an α-approximate distance from s to t in G-x for any given query (x, t) ∈ V × V. It is a data structure version of the so-called single-source replacement path problem (SSRP). In this paper, we present a new nearly linear-time algorithm of constructing a (1 + ε)-VSDO for any directed input graph with polynomially bounded integer edge weights. More precisely, the presented oracle attains Õ(m log (nW)/ ε + n log² (nW)/ε²) construction time, Õ(n log (nW) / ε) size, and Õ(1/ε) query time, where n is the number of vertices, m is the number of edges, and W is the maximum edge weight. These bounds are all optimal up to polylogarithmic factors. To the best of our knowledge, this is the first non-trivial algorithm for SSRP/VSDO beating Õ(mn) computation time for directed graphs with general edge weight functions, and also the first nearly linear-time construction breaking approximation factor 3. Such a construction has been unknown even for undirected and unweighted graphs. In addition, our result implies that the known conditional lower bounds for the exact SSRP computation does not apply to the case of approximation.
Cite as

Kaito Harada, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa. A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harada_et_al:LIPIcs.ESA.2024.65,
  author =	{Harada, Kaito and Kitamura, Naoki and Izumi, Taisuke and Masuzawa, Toshimitsu},
  title =	{{A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{65:1--65:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.65},
  URN =		{urn:nbn:de:0030-drops-211367},
  doi =		{10.4230/LIPIcs.ESA.2024.65},
  annote =	{Keywords: data structure, distance sensitivity oracle, replacement path problem, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.2
Partial Gathering of Mobile Agents in Dynamic Tori

Authors: Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, and Yonghwan Kim

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic tori. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all k agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer g (< k), that agents terminate in a configuration such that either at least g agents or no agent exists at each node. So far, in almost cases, the partial gathering problem has been considered in static graphs. As only one exception, it is considered in a kind of dynamic rings called 1-interval connected rings, that is, one of the links in the ring may be missing at each time step. In this paper, we consider partial gathering in another dynamic topology. Concretely, we consider it in n× n dynamic tori such that each of row rings and column rings is represented as a 1-interval connected ring. In such networks, when k = O(gn), focusing on the relationship between the values of k, n, and g, we aim to characterize the solvability of the partial gathering problem and analyze the move complexity of the proposed algorithms when the problem can be solved. First, we show that agents cannot solve the problem when k = o(gn), which means that Ω (gn) agents are necessary to solve the problem. Second, we show that the problem can be solved with the total number of O(gn³) moves when 2gn+2n-1 ≤ k ≤ 2gn + 6n +16g -12. Finally, we show that the problem can be solved with the total number of O(gn²) moves when k ≥ 2gn + 6n +16g -11. From these results, we show that our algorithms can solve the partial gathering problem in dynamic tori with the asymptotically optimal number Θ (gn) of agents. In addition, we show that agents require a total number of Ω(gn²) moves to solve the partial gathering problem in dynamic tori when k = Θ(gn). Thus, when k ≥ 2gn+6n+16g -11, our algorithm can solve the problem with asymptotically optimal number O(gn²) of agent moves.
Cite as

Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, and Yonghwan Kim. Partial Gathering of Mobile Agents in Dynamic Tori. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shibata_et_al:LIPIcs.SAND.2023.2,
  author =	{Shibata, Masahiro and Kitamura, Naoki and Eguchi, Ryota and Sudo, Yuichi and Nakamura, Junya and Kim, Yonghwan},
  title =	{{Partial Gathering of Mobile Agents in Dynamic Tori}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{2:1--2:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.2},
  URN =		{urn:nbn:de:0030-drops-179387},
  doi =		{10.4230/LIPIcs.SAND.2023.2},
  annote =	{Keywords: distributed system, mobile agents, partial gathering, dynamic tori}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.11
Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs

Authors: Taichi Inoue, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
We investigated the computational power of a single mobile agent in an n-node graph with storage (i.e., node memory). Generally, a system with one-bit agent memory and O(1)-bit storage is as powerful as that with O(n)-bit agent memory and O(1)-bit storage. Thus, we focus on the difference between one-bit memory and oblivious (i.e., zero-bit memory) agents. Although their computational powers are not equivalent, all the known results exhibiting such a difference rely on the fact that oblivious agents cannot transfer any information from one side to the other across the bridge edge. Hence, our main question is as follows: Are the computational powers of one-bit memory and oblivious agents equivalent in 2-edge-connected graphs or not? The main contribution of this study is to answer this question under the relaxed assumption that each node has O(logΔ)-bit storage (where Δ is the maximum degree of the graph). We present an algorithm for simulating any algorithm for a single one-bit memory agent using an oblivious agent with O(n²)-time overhead per round. Our results imply that the topological structure of graphs differentiating the computational powers of oblivious and non-oblivious agents is completely characterized by the existence of bridge edges.
Cite as

Taichi Inoue, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa. Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{inoue_et_al:LIPIcs.OPODIS.2022.11,
  author =	{Inoue, Taichi and Kitamura, Naoki and Izumi, Taisuke and Masuzawa, Toshimitsu},
  title =	{{Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.11},
  URN =		{urn:nbn:de:0030-drops-176311},
  doi =		{10.4230/LIPIcs.OPODIS.2022.11},
  annote =	{Keywords: mobile agent, depth-first search, space complexity}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.25
Low-Congestion Shortcut and Graph Parameters

Authors: Naoki Kitamura, Hirotaka Kitagawa, Yota Otachi, and Taisuke Izumi

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Omega~(sqrt{n} + D) rounds for many global problems, where n is the number of nodes and D is the diameter of the input graph. Since such a lower bound is derived from special "hard-core" instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts is initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. Specifically, given a specific graph class X, an f-round algorithm of constructing shortcuts of quality q for any instance in X results in O~(q + f)-round algorithms of solving several fundamental graph problems such as minimum spanning tree and minimum cut, for X. The main interest on this line is to identify the graph classes allowing the shortcuts which are efficient in the sense of breaking O~(sqrt{n}+D)-round general lower bounds. In this paper, we consider the relationship between the quality of low-congestion shortcuts and three major graph parameters, chordality, diameter, and clique-width. The main contribution of the paper is threefold: (1) We show an O(1)-round algorithm which constructs a low-congestion shortcut with quality O(kD) for any k-chordal graph, and prove that the quality and running time of this construction is nearly optimal up to polylogarithmic factors. (2) We present two algorithms, each of which constructs a low-congestion shortcut with quality O~(n^{1/4}) in O~(n^{1/4}) rounds for graphs of D=3, and that with quality O~(n^{1/3}) in O~(n^{1/3}) rounds for graphs of D=4 respectively. These results obviously deduce two MST algorithms running in O~(n^{1/4}) and O~(n^{1/3}) rounds for D=3 and 4 respectively, which almost close the long-standing complexity gap of the MST construction in small-diameter graphs originally posed by Lotker et al. [Distributed Computing 2006]. (3) We show that bounding clique-width does not help the construction of good shortcuts by presenting a network topology of clique-width six where the construction of MST is as expensive as the general case.
Cite as

Naoki Kitamura, Hirotaka Kitagawa, Yota Otachi, and Taisuke Izumi. Low-Congestion Shortcut and Graph Parameters. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{kitamura_et_al:LIPIcs.DISC.2019.25,
  author =	{Kitamura, Naoki and Kitagawa, Hirotaka and Otachi, Yota and Izumi, Taisuke},
  title =	{{Low-Congestion Shortcut and Graph Parameters}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.25},
  URN =		{urn:nbn:de:0030-drops-113328},
  doi =		{10.4230/LIPIcs.DISC.2019.25},
  annote =	{Keywords: distributed graph algorithms, low-congestion shortcut, k-chordal graph, clique width, minimum spanning tree}
}
Document
DOI: 10.4230/LIPIcs.FUN.2018.26
Uniform Distribution On Pachinko

Authors: Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
Pachinko is a japanese mechanical gambling game similar to pinball. Recently, Akitaya et al. proposed several mathematical models of Pachinko. A number of pins are spiked in a field. A ball drops from the top-side end of the playfield, and falls down. In the 50-50 model, if the ball hits a pin, it moves to the left or right of the pin with equal probability. An arrangement of pins generates a distribution of the drop probability over all columns. We consider the problem of generating uniform distributions. Akitaya et al. show that (1/2^{{a}})-uniform distribution is possible for {a} in {0,1,2,3,4} and conjectured that it is possible for any positive integer a. In this paper, we show that the conjecture is true by a constructive way.
Cite as

Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi. Uniform Distribution On Pachinko. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{kitamura_et_al:LIPIcs.FUN.2018.26,
  author =	{Kitamura, Naoki and Kawabata, Yuya and Izumi, Taisuke},
  title =	{{Uniform Distribution On Pachinko}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.26},
  URN =		{urn:nbn:de:0030-drops-88170},
  doi =		{10.4230/LIPIcs.FUN.2018.26},
  annote =	{Keywords: Pachinko, discrete mathematics}
}
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