arXiv subjects

Fukuhito Ooshita

Publications and source records attributed to Fukuhito Ooshita.

At least 19 recordsLinked to original sources

arXiv2026

A Nearly Time-Optimal Population Protocol for Self-Stabilizing Leader Election on Rings with Polylogarithmic States

We propose a self-stabilizing leader election (SS-LE) protocol on ring networks in the population protocol model. Given an integer $ψ$ satisfying $\log n \le ψ\le \log n+O(1)$, where $n$ is the population size, the proposed protocol reaches a safe configuration within $O(n^2 \log n)$ steps with high probability from any initial configuration, and thereafter preserves the same unique leader forever. Since no protocol solves SS-LE in $o(n^2)$ steps with high probability, the convergence time is near-optimal, with only an $O(\log n)$ multiplicative gap. The proposed protocol uses only $\mathit{polylog}(n)$ states. Two state-of-the-art protocols are known for SS-LE on ring networks. The first protocol uses a polynomial number of states and solves SS-LE in $O(n^2)$ steps, whereas the second protocol requires super-exponential time but uses only a constant number of states. Our proposed protocol provides a useful middle ground between these two approaches.

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arXiv2025

The R(1)W(1) Communication Model for Self-Stabilizing Distributed Algorithms

Self-stabilization is a versatile methodology in the design of fault-tolerant distributed algorithms for transient faults. A self-stabilizing system automatically recovers from any kind and any finite number of transient faults. This property is specifically useful in modern distributed systems with a large number of components. In this paper, we propose a new communication and execution model named the R(1)W(1) model in which each process can read and write its own and neighbors' local variables in a single step. We propose self-stabilizing distributed algorithms in the R(1)W(1) model for the problems of maximal matching, minimal k-dominating set and maximal k-dependent set. Finally, we propose an example transformer, based on randomized distance-two local mutual exclusion, to simulate algorithms designed for the R(1)W(1) model in the synchronous message passing model with synchronized clocks.

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arXiv2025

Time- and Space-Optimal Silent Self-Stabilizing Exact Majority in Population Protocols

We address the self-stabilizing exact majority problem in the population protocol model, introduced by Angluin, Aspnes, Diamadi, Fischer, and Peralta (2004). In this model, there are $n$ state machines, called agents, which form a network. At each time step, only two agents interact with each other, and update their states. In the self-stabilizing exact majority problem, each agent has a fixed opinion, $\mathtt{A}$ or $\mathtt{B}$, and stabilizes to a safe configuration in which all agents output the majority opinion from any initial configuration. In this paper, we show the impossibility of solving the self-stabilizing exact majority problem without knowledge of $n$ in any protocol. We propose a silent self-stabilizing exact majority protocol, which stabilizes within $O(n)$ parallel time in expectation and within $O(n \log n)$ parallel time with high probability, using $O(n)$ states, with knowledge of $n$. Here, a silent protocol means that, after stabilization, the state of each agent does not change. We establish lower bounds, proving that any silent protocol requires $Ω(n)$ states, $Ω(n)$ parallel time in expectation, and $Ω(n \log n)$ parallel time with high probability to reach a safe configuration. Thus, the proposed protocol is time- and space-optimal.

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arXiv2025

Self-stabilizing Graph Exploration by a Single Agent

In this paper, we present two self-stabilizing algorithms that enable a single (mobile) agent to explore graphs. Starting from any initial configuration, \ie regardless of the initial states of the agent and all nodes, as well as the initial location of the agent, the algorithms ensure the agent visits all nodes. We evaluate the algorithms based on two metrics: the \emph{cover time}, defined as the number of moves required to visit all nodes, and \emph{memory usage}, defined as the storage needed for maintaining the states of the agent and each node. The first algorithm is randomized. Given an integer $c = Ω(n)$, its cover time is optimal, \ie $O(m)$ in expectation, and its memory requirements are $O(\log c)$ bits for the agent and $O(\log (c+δ_v))$ bits for each node $v$, where $n$ and $m$ are the numbers of nodes and edges, respectively, and $δ_v$ is the degree of node $v$. For general $c \ge 2$, its cover time is $O( m \cdot \min(D, \frac{n}{c}+1, \frac{D}{c} + \log n))$, where $D$ is the diameter of a graph. The second algorithm is deterministic. It requires an input integer $k \ge \max(D, \dmax)$, where $\dmax$ is the maximum degree of the graph. The cover time of this algorithm is $O(m + nD)$, and it uses $O(\log k)$ bits of memory for both the agent and each node.

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arXiv2024

Stand-Up Indulgent Gathering on Lines for Myopic Luminous Robots

We consider a strong variant of the crash fault-tolerant gathering problem called stand-up indulgent gathering (SUIG), by robots endowed with limited visibility sensors and lights on line-shaped networks. In this problem, a group of mobile robots must eventually gather at a single location, not known beforehand, regardless of the occurrence of crashes. Differently from previous work that considered unlimited visibility, we assume that robots can observe nodes only within a certain fixed distance (that is, they are myopic), and emit a visible color from a fixed set (that is, they are luminous), without multiplicity detection. We consider algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots. Then, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, SUIG can be solved in the fully synchronous model.

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arXiv2023

Meeting Times of Non-atomic Random Walks

In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected times until they meet when the two agents are initially located at different vertices. A key feature of the problem is that, in each discrete time-clock (called \textit{round}) of the process, the scheduler selects only one of the two agents, and the agent performs one move of the random walk. In the adversarial setting, the scheduler utilizes the strategy that intends to \textit{maximizing} the expected time to meet. In the seminal papers \cite{collisions,israeli1990token,tetali1993simult}, for the random walks of two agents, the notion of \textit{atomicity} is implicitly considered. That is, each move of agents should complete while the other agent waits. In this paper, we consider and formalize the meeting time of \textit{non-atomic} random walks. In the non-atomic random walks, we assume that in each round, only one agent can move but the move does not necessarily complete in the next round. In other words, we assume that an agent can move at a round while the other agent is still moving on an edge. For the non-atomic random walks with the adversarial schedulers, we give a polynomial upper bound on the meeting times.

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arXiv2022

Gathering despite a linear number of weakly Byzantine agents

We study the gathering problem to make multiple agents initially scattered in arbitrary networks gather at a single node. There exist $k$ agents with unique identifiers (IDs) in the network, and $f$ of them are weakly Byzantine agents, which behave arbitrarily except for falsifying their IDs. The agents behave in synchronous rounds, and each node does not have any memory like a whiteboard. In the literature, there exists a gathering algorithm that tolerates any number of Byzantine agents, while the fastest gathering algorithm requires $Ω(f^2)$ non-Byzantine agents. This paper proposes an algorithm that solves the gathering problem efficiently with $Ω(f)$ non-Byzantine agents since there is a large gap between the number of non-Byzantine agents in previous works. The proposed algorithm achieves the gathering in $O(f\cdot|Λ_{good}|\cdot X(N))$ rounds in case of $9f+8\leq k$ and simultaneous startup if $N$ is given to agents, where $|Λ_{good}|$ is the length of the largest ID among non-Byzantine agents, and $X(n)$ is the number of rounds required to explore any network composed of $n$ nodes. This algorithm is faster than the most fault-tolerant existing algorithm and requires fewer non-Byzantine agents than the fastest algorithm if $n$ is given to agents, although the guarantees on simultaneous termination and startup delay are not the same. To achieve this property, we propose a new technique to simulate a Byzantine consensus algorithm for synchronous message-passing systems on agent systems.

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arXiv2021

Population Protocols for Graph Class Identification Problems

In this paper, we focus on graph class identification problems in the population protocol model. A graph class identification problem aims to decide whether a given communication graph is in the desired class (e.g. whether the given communication graph is a ring graph). Angluin et al. proposed graph class identification protocols with directed graphs and designated initial states under global fairness [Angluin et al., DCOSS2005]. We consider graph class identification problems for undirected graphs on various assumptions such as initial states of agents, fairness of the execution, and initial knowledge of agents. In particular, we focus on lines, rings, $k$-regular graphs, stars, trees, and bipartite graphs. With designated initial states, we propose graph class identification protocols for $k$-regular graphs, and trees under global fairness, and propose a graph class identification protocol for stars under weak fairness. Moreover, we show that, even if agents know the number of agents $n$, there is no graph class identification protocol for lines, rings, $k$-regular graphs, trees, or bipartite graphs under weak fairness. On the other hand, with arbitrary initial states, we show that there is no graph class identification protocol for lines, rings, $k$-regular graphs, stars, trees, or bipartite graphs.

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arXiv2021

Terminating grid exploration with myopic luminous robots

We investigate the terminating grid exploration for autonomous myopic luminous robots. Myopic robots mean that they can observe nodes only within a certain fixed distance, and luminous robots mean that they have light devices that can emit colors. First, we prove that, in the semi-synchronous and asynchronous models, three myopic robots are necessary to achieve the terminating grid exploration if the visible distance is one. Next, we give fourteen algorithms for the terminating grid exploration in various assumptions of synchrony (fully-synchronous, semi-synchronous, and asynchronous models), visible distance, the number of colors, and a chirality. Six of them are optimal in terms of the number of robots.

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arXiv2021

Asynchronous Gathering in a Torus

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other, but are endowed with visibility sensors that allow them to see the positions of the other robots. Most of the investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configuration. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robots unless it is their current node. As a consequence, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network.

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arXiv2020

Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs

In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of \emph{arbitrary} communication graphs. As a result, we clarify the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight.

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arXiv2020

Gathering with a strong team in weakly Byzantine environments

We study the gathering problem requiring a team of mobile agents to gather at a single node in arbitrary networks. The team consists of $k$ agents with unique identifiers (IDs), and $f$ of them are weakly Byzantine agents, which behave arbitrarily except falsifying their identifiers. The agents move in synchronous rounds and cannot leave any information on nodes. If the number of nodes $n$ is given to agents, the existing fastest algorithm tolerates any number of weakly Byzantine agents and achieves gathering with simultaneous termination in $O(n^4\cdot|Λ_{good}|\cdot X(n))$ rounds, where $|Λ_{good}|$ is the length of the maximum ID of non-Byzantine agents and $X(n)$ is the number of rounds required to explore any network composed of $n$ nodes. In this paper, we ask the question of whether we can reduce the time complexity if we have a strong team, i.e., a team with a few Byzantine agents, because not so many agents are subject to faults in practice. We give a positive answer to this question by proposing two algorithms in the case where at least $4f^2+9f+4$ agents exist. Both the algorithms take the upper bound $N$ of $n$ as input. The first algorithm achieves gathering with non-simultaneous termination in $O((f+|Λ_{good}|)\cdot X(N))$ rounds. The second algorithm achieves gathering with simultaneous termination in $O((f+|Λ_{all}|)\cdot X(N))$ rounds, where $|Λ_{all}|$ is the length of the maximum ID of all agents. The second algorithm significantly reduces the time complexity compared to the existing one if $n$ is given to agents and $|Λ_{all}|=O(|Λ_{good}|)$ holds.

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arXiv2019

Uniform Partition in Population Protocol Model under Weak Fairness

We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k=2 (called uniform bipartition), a previous work clarified space complexity under various assumptions: 1) an initialized base station (BS) or no BS, 2) weak or global fairness, 3) designated or arbitrary initial states of agents, and 4) symmetric or asymmetric protocols, except for the setting that agents execute a protocol from arbitrary initial states under weak fairness in the model with an initialized base station. In this paper, we clarify the space complexity for this remaining setting. In this setting, we prove that P states are necessary and sufficient to realize asymmetric protocols, and that P+1 states are necessary and sufficient to realize symmetric protocols, where P is the known upper bound of the number of agents. From these results and the previous work, we have clarified the solvability of the uniform bipartition for each combination of assumptions. Additionally, we newly consider an assumption on a model of a non-initialized BS and clarify solvability and space complexity in the assumption. Moreover, the results in this paper can be applied to the case that k is an arbitrary integer (called uniform k-partition).

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arXiv2019

Gathering on Rings for Myopic Asynchronous Robots with Lights

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility.

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arXiv2019

Logarithmic Expected-Time Leader Election in Population Protocol Model

In this paper, the leader election problem in the population protocol model is considered. A leader election protocol with logarithmic stabilization time is given. Given a rough knowledge m of the population size n such that m >= \log_2 n and m=O(log n), the proposed protocol guarantees that exactly one leader is elected from n agents within O(log n) parallel time in expectation and the unique leader is kept forever thereafter. The number of states per agent of the protocol is O(log n).

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arXiv2019

Neighborhood Mutual Remainder: Self-Stabilizing Implementation of Look-Compute-Move Robots (Extended Abstract)

Local mutual exclusion guarantees that no two neighboring processes enter a critical section at the same time while satisfying both mutual exclusion and no starvation properties. On the other hand, processes may want to execute some operation simultaneously with the neighbors. Of course, we can use a globally synchronized clock to achieve the task but it is very expensive to realize it in a distributed system in general. In this paper, we define a new concept neighborhood mutual remainder. A distributed algorithm that satisfies the neighborhood mutual remainder requirement should satisfy global fairness, l-exclusion and repeated local rendezvous requirements. Global fairness is satisfied when each process (that requests to enter the critical section infinitely often) executes the critical section infinitely often, l-exclusion is satisfied when at most l neighboring processes enter the critical section at the same time, and repeated local rendezvous is satisfied when for each process infinitely often no process in the closed neighborhood is in the critical or trying section. We first formalize the concept of neighborhood mutual remainder, and give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve neighborhood mutual remainder. We also present two applications of neighborhood mutual remainder to a Look-Compute-Move robot system. One is for implementing a move-atomic property and the other is for implementing FSYNC scheduler, where robots possess an independent clock that is advanced in the same speed. These are the first self-stabilizing implementations of the LCM synchronization.

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arXiv2018

Ring Exploration with Myopic Luminous Robots

We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Different from the usual Look-Compute-Move (LCM) model, we consider two characteristics: myopia and luminosity. Myopia means each robot has a limited visibility. We consider the weakest assumption for myopia: each robot can only observe its neighboring nodes. Luminosity means each robot maintains a non-volatile visible light. We consider the weakest assumption for luminosity: each robot can use only two colors for its light. The main interest of this paper is to clarify the impact of luminosity on exploration with myopic robots. As a main contribution, we prove that 1) in the fully synchronous model, two and three robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively, and 2) in the semi-synchronous and asynchronous models, three and four robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively. These results clarify the power of lights for myopic robots since, without lights, five robots are necessary and sufficient to achieve terminating exploration in the fully synchronous model, and no terminating exploration algorithm exists in the semi-synchronous and asynchronous models. We also show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), the proposed perpetual exploration algorithm is universal, that is, the algorithm solves perpetual exploration from any solvable initial configuration with two (resp., three) robots and two colors. On the other hand, we show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), no universal algorithm exists for terminating exploration, that is, no algorithm may solve terminating exploration from any solvable initial configuration with three (resp., four) robots and two colors.

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arXiv2015

Partial Gathering of Mobile Agents in Asynchronous Rings

In this paper, we consider the partial gathering problem of mobile agents in asynchronous unidirectional rings equipped with whiteboards on nodes. The partial gathering problem is a new generalization of the total gathering problem. The partial gathering problem requires, for a given integer $g$, that each agent should move to a node and terminate so that at least $g$ agents should meet at the same node. The requirement for the partial gathering problem is weaker than that for the (well-investigated) total gathering problem, and thus, we have interests in clarifying the difference on the move complexity between them. We propose three algorithms to solve the partial gathering problem. The first algorithm is deterministic but requires unique ID of each agent. This algorithm achieves the partial gathering in $O(gn)$ total moves, where $n$ is the number of nodes. The second algorithm is randomized and requires no unique ID of each agent (i.e., anonymous). This algorithm achieves the partial gathering in expected $O(gn)$ total moves. The third algorithm is deterministic and requires no unique ID of each agent. For this case, we show that there exist initial configurations in which no algorithm can solve the problem and agents can achieve the partial gathering in $O(kn)$ total moves for solvable initial configurations, where $k$ is the number of agents. Note that the total gathering problem requires $Ω(kn)$ total moves, while the partial gathering problem requires $Ω(gn)$ total moves in each model. Hence, we show that the move complexity of the first and second algorithms is asymptotically optimal.

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