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Yuichi Sudo

Publications and source records attributed to Yuichi Sudo.

At least 19 recordsLinked to original sources
arXiv2026

The Maximum Mutual Visibility Set on a Cactus Graph and the Self-stabilizing Constructions

Given a graph $G=(V,E)$, let $S$ ($\subseteq V$) be a set of vertices. Two vertices are \emph{mutually visible} if there exists a shortest path in $G$ between them that does not contain any other vertex of $S$. A set $S$ is a \emph{Mutual Visibility Set} (\MVS) if every pair of vertices in $S$ is mutually visible. The concept of \MVS s in graphs has attracted significant attention since its introduction, as it provides an important structural property of graphs. However, determining a maximum \MVS\ in general graphs is computationally intractable; the decision problem of whether a graph admits an \MVS\ of size at least $k$ has been shown to be \emph{NP-complete}. Thus, prior work has focused on finding maximal \MVS s or restricting attention to specific graph classes. Cactus graphs form a fundamental low-treewidth class, yet the maximum \MVS\ problem for this class remains open. In this paper, we first determine the size of maximum \MVS~in cactus graphs, and introduce two self-stabilizing algorithms that construct such sets. The first algorithm uses a single BFS tree and stabilizes in $O(D)$ rounds with $O(\log n)$ bits per process on average; the second one uses parallel BFS trees and stabilizes in $O(|C_{\max}|+|T_{\max}|)$ rounds, which we show to be asymptotically tight as a function of these two parameters, even on graphs where $|C_{\max}|+|T_{\max}| = o(D)$.

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arXiv2026

Tight Bounds on Window Size and Time for Single-Agent Graph Exploration under T-Interval Connectivity

We study deterministic exploration by a single agent in $T$-interval-connected graphs, a standard model of dynamic networks in which, for every time window of length $T$, the intersection of the graphs within the window is connected. The agent does not know the window size $T$, nor the number of nodes $n$ or edges $m$, and must visit all nodes of the graph. We consider two visibility models, $KT_0$ and $KT_1$, depending on whether the agent can observe the identifiers of neighboring nodes. We investigate two fundamental questions: the minimum window size that guarantees exploration, and the optimal exploration time under sufficiently large window size. For both models, we show that a window size $T = \Omega(m)$ is necessary. We also present deterministic algorithms whose required window size is $O(\epsilon(n,m)\cdot m + n \log^2 n)$, where $\epsilon(n,m) = \frac{\ln n}{1 + \ln m - \ln n}$. These bounds are tight for a wide range of $m$, in particular when $m = n^{1+\Theta(1)}$. The same algorithms also yield optimal or near-optimal exploration time: we prove lower bounds of $\Omega((m - n + 1)n)$ in the $KT_0$ model and $\Omega(m)$ in the $KT_1$ model, and show that our algorithms match these bounds up to a polylogarithmic factor, while being fully time-optimal when $m = n^{1+\Theta(1)}$. This yields tight bounds when parameterized solely by $n$: $\Theta(n^3)$ for $KT_0$ and $\Theta(n^2)$ for $KT_1$.

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arXiv2025

Two-Robot Computational Landscape: A Complete Characterization of Model Power in Minimal Mobile Robot Systems

The computational power of autonomous mobile robots under the Look-Compute-Move (LCM) model has been widely studied through an extensive hierarchy of robot models defined by the presence of memory, communication, and synchrony assumptions. While the general n-robot landscape has been largely established, the exact structure for two robots has remained unresolved. This paper presents the first complete characterization of the computational power of two autonomous robots across all major models, namely OBLOT, FSTA, FCOM, and LUMI, under the full spectrum of schedulers (FSYNCH, SSYNCH, ASYNCH, and their atomic variants). Our results reveal a landscape that fundamentally differs from the general case. Most notably, we prove that FSTA^F and LUMI^F coincide under full synchrony, a surprising collapse indicating that perfect synchrony can substitute both memory and communication when only two robots exist. We also show that FSTA and FCOM are orthogonal: there exists a problem solvable in the weakest communication model but impossible even in the strongest finite-state model, completing the bidirectional incomparability. All equivalence and separation results are derived through a novel simulation-free method, providing a unified and constructive view of the two-robot hierarchy. This yields the first complete and exact computational landscape for two robots, highlighting the intrinsic challenges of coordination at the minimal scale.

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arXiv2025

Complementary Time-Space Tradeoff for Self-Stabilizing Leader Election: Polynomial States Meet Sublinear Time

We study the self-stabilizing leader election (SS-LE) problem in the population protocol model, assuming exact knowledge of the population size $n$. Burman, Chen, Chen, Doty, Nowak, Severson, and Xu [BCC+21a] (PODC) showed that this problem can be solved in $O(n)$ expected time with $O(n)$ states. Recently, G\k{a}sieniec, Grodzicki, and Stachowiak [GGS25] (PODC) proved that $n+O(\log n)$ states suffice to achieve $O(n \log n)$ time both in expectation and with high probability (w.h.p.). If substantially more states are available, sublinear time can be achieved. The authors of [BCC+21] presented a $2^{O(n^\rho\log n)}$-state SS-LE protocol with a parameter $\rho$: setting $\rho = \Theta(\log n)$ yields an optimal $O(\log n)$ time both in expectation and w.h.p., while $\rho = \Theta(1)$ results in $O(\rho\,n^{1/(\rho+1)})$ expected time. Recently, Austin, Berenbrink, Friedetzky, G\"otte, and Hintze [ABF+25] (PODC) presented a novel SS-LE protocol parameterized by a positive integer $\rho$ with $1 \le \rho < n/2$ that solves SS-LE in $O(\frac{n}{\rho}\cdot\log n)$ time w.h.p.\ using $2^{O(\rho^2\log n)}$ states. This paper independently presents yet another time--space tradeoff of SS-LE: for any positive integer $\rho$ with $2 \le \rho \le \sqrt{n}$, SS-LE can be achieved within $O\left(\frac{n}{\rho}\cdot \log\rho\right)$ expected time using $2^{2\rho\lg^2\rho + O(\log n)}$ states. The proposed protocol uses significantly fewer states than [ABF+25] for any expected stabilization time above $\Theta(\sqrt{n}\log n)$. When $\rho = \Theta\left(\frac{\log n}{\log^2 \log n}\right)$, the proposed protocol is the first to achieve sublinear time while using only polynomially many states. A limitation of our protocol is that the constraint $\rho\le\sqrt{n}$ prevents achieving $o(\sqrt{n}\log n)$ time, whereas the protocol of [ABF+25] can surpass this bound.

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arXiv2025

Recolorable Graph Exploration by an Oblivious Agent with Fewer Colors

Recently, B\"ockenhauer, Frei, Unger, and Wehner (SIROCCO 2023) introduced a novel variant of the graph exploration problem in which a single memoryless agent must visit all nodes of an unknown, undirected, and connected graph before returning to its starting node. Unlike the standard model for mobile agents, edges are not labeled with port numbers. Instead, the agent can color its current node and observe the color of each neighboring node. To move, it specifies a target color and then moves to an adversarially chosen neighbor of that color. B\"ockenhauer~et al.~analyzed the minimum number of colors required for successful exploration and proposed an elegant algorithm that enables the agent to explore an arbitrary graph using only eight colors. In this paper, we present a novel graph exploration algorithm that requires only six colors. Furthermore, we prove that five colors are sufficient if we consider only a restricted class of graphs, which we call the $\varphi$-free graphs, a class that includes every graph with maximum degree at most three and every cactus.

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arXiv2025

Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents

We study the \emph{Byzantine} gathering problem involving $k$ mobile agents with unique identifiers (IDs), $f$ of which are Byzantine. These agents start the execution of a common algorithm from (possibly different) nodes in an $n$-node network, potentially starting at different times. Once started, the agents operate in synchronous rounds. We focus on \emph{weakly} Byzantine environments, where Byzantine agents can behave arbitrarily but cannot falsify their IDs. The goal is for all \emph{non-Byzantine} agents to eventually terminate at a single node simultaneously. In this paper, we first prove two impossibility results: (1) for any number of non-Byzantine agents, no algorithm can solve this problem without global knowledge of the network size or the number of agents, and (2) no self-stabilizing algorithm exists if $k\leq 2f$ even with $n$, $k$, $f$, and the length $\Lambda_g$ of the largest ID among IDs of non-Byzantine agents, where the self-stabilizing algorithm enables agents to gather starting from arbitrary (inconsistent) initial states. Next, based on these results, we introduce a \emph{perpetual gathering} problem and propose a self-stabilizing algorithm for this problem. This problem requires that all non-Byzantine agents always be co-located from a certain time onwards. If the agents know $\Lambda_g$ and upper bounds $N$, $K$, $F$ on $n$, $k$, $f$, the proposed algorithm works in $O(K\cdot F\cdot \Lambda_g\cdot X(N))$ rounds, where $X(n)$ is the time required to visit all nodes in a $n$-nodes network. Our results indicate that while no algorithm can solve the original self-stabilizing gathering problem for any $k$ and $f$ even with \emph{exact} global knowledge of the network size and the number of agents, the self-stabilizing perpetual gathering problem can always be solved with just upper bounds on this knowledge.

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arXiv2024

Sublinear-time Collision Detection with a Polynomial Number of States in Population Protocols

This paper addresses the collision detection problem in population protocols. The network consists of state machines called agents. At each time step, exactly one pair of agents is chosen uniformly at random to have an interaction, changing the states of the two agents. The collision detection problem involves each agent starting with an input integer between $1$ and $n$, where $n$ is the number of agents, and requires those agents to determine whether there are any duplicate input values among all agents. Specifically, the goal is for all agents to output false if all input values are distinct, and true otherwise. In this paper, we present an algorithm that requires a polynomial number of states per agent and solves the collision detection problem with probability one in sub-linear parallel time, both with high probability and in expectation. To the best of our knowledge, this algorithm is the first to solve the collision detection problem using a polynomial number of states within sublinear parallel time, affirmatively answering the question raised by Burman, Chen, Chen, Doty, Nowak, Severson, and Xu [PODC 2021] for the first time.

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arXiv2024

Complete Graph Identification in Population Protocols

We consider the population protocol model where indistinguishable state machines, referred to as agents, communicate in pairs. The communication graph specifies potential interactions (\ie communication) between agent pairs. This paper addresses the complete graph identification problem, requiring agents to determine if their communication graph is a clique or not. We evaluate various settings based on: (i) the fairness preserved by the adversarial scheduler -- either global fairness or weak fairness, and (ii) the knowledge provided to agents beforehand -- either the exact population size $n$, a common upper bound $P$ on $n$, or no prior information. Positively, we show that $O(n^2)$ states per agent suffice to solve the complete graph identification problem under global fairness without prior knowledge. With prior knowledge of $n$, agents can solve the problem using only $O(n)$ states under weak fairness. Negatively, we prove that complete graph identification remains unsolvable under weak fairness when only a common upper bound $P$ on the population size $n$ is known.

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arXiv2023

On Asynchrony, Memory, and Communication: Separations and Landscapes

Research on distributed computing by a team of identical mobile computational entities, called robots, operating in a Euclidean space in $\mathit{Look}$-$\mathit{Compute}$-$\mathit{Move}$ ($\mathit{LCM}$) cycles, has recently focused on better understanding how the computational power of robots depends on the interplay between their internal capabilities (i.e., persistent memory, communication), captured by the four standard computational models (OBLOT, LUMI, FSTA, and FCOM) and the conditions imposed by the external environment, controlling the activation of the robots and their synchronization of their activities, perceived and modeled as an adversarial scheduler. We consider a set of adversarial asynchronous schedulers ranging from the classical semi-synchronous (SSYNCH) and fully asynchronous (ASYNCH) settings, including schedulers (emerging when studying the atomicity of the combination of operations in the $\mathit{LCM}$ cycles) whose adversarial power is in between those two. We ask the question: what is the computational relationship between a model $M_1$ under adversarial scheduler $K_1$ ($M_1(K_1)$) and a model $M_2$ under scheduler $K_2$ ($M_2(K_2)$)? For example, are the robots in $M_1(K_1)$ more powerful (i.e., they can solve more problems) than those in $M_2(K_2)$? We answer all these questions by providing, through cross-model analysis, a complete characterization of the computational relationship between the power of the four models of robots under the considered asynchronous schedulers. In this process, we also provide qualified answers to several open questions, including the outstanding one on the proper dominance of SSYNCH over ASYNCH in the case of unrestricted visibility.

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arXiv2023

Near-linear Time Dispersion of Mobile Agents

Consider that there are $k\le n$ agents in a simple, connected, and undirected graph $G=(V,E)$ with $n$ nodes and $m$ edges. The goal of the dispersion problem is to move these $k$ agents to mutually distinct nodes. Agents can communicate only when they are at the same node, and no other communication means, such as whiteboards, are available. We assume that the agents operate synchronously. We consider two scenarios: when all agents are initially located at a single node (rooted setting) and when they are initially distributed over one or more nodes (general setting). Kshemkalyani and Sharma presented a dispersion algorithm for the general setting, which uses $O(m_k)$ time and $\log(k + \Delta)$ bits of memory per agent [OPODIS 2021], where $m_k$ is the maximum number of edges in any induced subgraph of $G$ with $k$ nodes, and $\Delta$ is the maximum degree of $G$. This algorithm is currently the fastest in the literature, as no $o(m_k)$-time algorithm has been discovered, even for the rooted setting. In this paper, we present significantly faster algorithms for both the rooted and the general settings. First, we present an algorithm for the rooted setting that solves the dispersion problem in $O(k\log \min(k,\Delta))=O(k\log k)$ time using $O(\log (k+\Delta))$ bits of memory per agent. Next, we propose an algorithm for the general setting that achieves dispersion in $O(k \log k \cdot \log \min(k,\Delta))=O(k \log^2 k)$ time using $O(\log (k+\Delta))$ bits. Finally, for the rooted setting, we give a time-optimal (i.e.,~$O(k)$-time) algorithm with $O(\Delta+\log k)$ bits of space per agent. All algorithms presented in this paper work only in the synchronous setting, while several algorithms in the literature, including the one given by Kshemkalyani and Sharma at OPODIS 2021, work in the asynchronous setting.

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arXiv2023

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 $\psi$ satisfying $\log n \le \psi \le \log n+O(1)$, 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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arXiv2022

Partial gathering of mobile agents in dynamic rings

In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic bidirectional ring networks. When k agents are distributed in the network, 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, the partial gathering problem has been considered in static graphs. In this paper, we start considering partial gathering in dynamic graphs. As a first step, we consider this problem in 1-interval connected rings, that is, one of the links in a ring may be missing at each time step. In such networks, focusing on the relationship between the values of k and g, we fully 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 the g-partial gathering problem is unsolvable when k <= 2g. Second, we show that the problem can be solved with O(n log g) time and the total number of O(gn log g) moves when 2g + 1 <= k <= 3g - 2. Third, we show that the problem can be solved with O(n) time and the total number of O(kn) moves when 3g - 1 <= k <= 8g - 4. Notice that since k = O(g) holds when 3g - 1 <= k <= 8g - 4, the move complexity O(kn) in this case can be represented also as O(gn). Finally, we show that the problem can be solved with O(n) time and the total number of O(gn) moves when k >= 8g - 3. These results mean that the partial gathering problem can be solved also in dynamic rings when k >= 2g + 1. In addition, agents require a total number of \Omega(gn) moves to solve the partial (resp., total) gathering problem. Thus, when k >= 3g - 1, agents can solve the partial gathering problem with the asymptotically optimal total number of O(gn) moves.

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arXiv2022

Gathering Despite Defected View

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and to clarify the relation between the capabilities of robots and solvability of the problems is an emerging issue for a recent couple of decades. Generally, each robot can observe all other robots as long as there are no restrictions for visibility range or obstructions, regardless of the number of robots. In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We call this new computational model defected view model. Under this model, in this paper, we consider the gathering problem that requires all the robots to gather at the same point and propose two algorithms to solve the gathering problem in the adversarial ($N$,$N-2$)-defected model for $N \geq 5$ (where each robot observes at most $N-2$ robots chosen adversarially) and the distance-based (4,2)-defected model (where each robot observes at most 2 closest robots to itself) respectively, where $N$ is the number of robots. Moreover, we present an impossibility result showing that there is no (deterministic) gathering algorithm in the adversarial or distance-based (3,1)-defected model. Moreover, we show an impossibility result for the gathering in a relaxed ($N$, $N-2$)-defected model.

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arXiv2021

Smoothed Analysis of Population Protocols

In this work, we initiate the study of \emph{smoothed analysis} of population protocols. We consider a population protocol model where an adaptive adversary dictates the interactions between agents, but with probability $p$ every such interaction may change into an interaction between two agents chosen uniformly at random. That is, $p$-fraction of the interactions are random, while $(1-p)$-fraction are adversarial. The aim of our model is to bridge the gap between a uniformly random scheduler (which is too idealistic) and an adversarial scheduler (which is too strict). We focus on the fundamental problem of leader election in population protocols. We show that, for a population of size $n$, the leader election problem can be solved in $O(p^{-2}n \log^3 n)$ steps with high probability, using $O((\log^2 n) \cdot (\log (n/p)))$ states per agent, for \emph{all} values of $p\leq 1$. Although our result does not match the best known running time of $O(n \log n)$ for the uniformly random scheduler ($p=1$), we are able to present a \emph{smooth transition} between a running time of $O(n \cdot \mathrm{polylog} n)$ for $p=1$ and an infinite running time for the adversarial scheduler ($p=0$), where the problem cannot be solved. The key technical contribution of our work is a novel \emph{phase clock} algorithm for our model. This is a key primitive for much-studied fundamental population protocol algorithms (leader election, majority), and we believe it is of independent interest.

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arXiv2021

Gathering of seven autonomous mobile robots on triangular grids

In this paper, we consider the gathering problem of seven autonomous mobile robots on triangular grids. The gathering problem requires that, starting from any connected initial configuration where a subgraph induced by all robot nodes (nodes where a robot exists) constitutes one connected graph, robots reach a configuration such that the maximum distance between two robots is minimized. For the case of seven robots, gathering is achieved when one robot has six adjacent robot nodes (they form a shape like a hexagon). In this paper, we aim to clarify the relationship between the capability of robots and the solvability of gathering on a triangular grid. In particular, we focus on visibility range of robots. To discuss the solvability of the problem in terms of the visibility range, we consider strong assumptions except for visibility range. Concretely, we assume that robots are fully synchronous and they agree on the direction and orientation of the x-axis, and chirality in the triangular grid. In this setting, we first consider the weakest assumption about visibility range, i.e., robots with visibility range 1. In this case, we show that there exists no collision-free algorithm to solve the gathering problem. Next, we extend the visibility range to 2. In this case, we show that our algorithm can solve the problem from any connected initial configuration. Thus, the proposed algorithm is optimal in terms of visibility range.

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arXiv2020

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 $c = \Omega(n)$, its cover time is optimal, \ie $O(m)$ in expectation, and its memory requirements are $O(\log c)$ bits for the agent and $O(\log (c+\delta_v))$ bits for each node $v$, where $n$ and $m$ are the numbers of nodes and edges, respectively, and $\delta_v$ 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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arXiv2020

Time-Optimal Self-Stabilizing Leader Election on Rings in Population Protocols

We propose a self-stabilizing leader election protocol on directed rings in the model of population protocols. Given an upper bound $N$ on the population size $n$, the proposed protocol elects a unique leader within $O(nN)$ expected steps starting from any configuration and uses $O(N)$ states. This convergence time is optimal if a given upper bound $N$ is asymptotically tight, i.e., $N=O(n)$.

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arXiv2020

Self-Stabilizing Construction of a Minimal Weakly $\mathcal{ST}$-Reachable Directed Acyclic Graph

We propose a self-stabilizing algorithm to construct a minimal weakly $\mathcal{ST}$-reachable directed acyclic graph (DAG), which is suited for routing messages on wireless networks. Given an arbitrary, simple, connected, and undirected graph $G=(V, E)$ and two sets of nodes, senders $\mathcal{S} (\subset V)$ and targets $\mathcal{T} (\subset V)$, a directed subgraph $\vec{G}$ of $G$ is a weakly $\mathcal{ST}$-reachable DAG on $G$, if $\vec{G}$ is a DAG and every sender can reach at least one target, and every target is reachable from at least one sender in $\vec{G}$. We say that a weakly $\mathcal{ST}$-reachable DAG $\vec{G}$ on $G$ is minimal if any proper subgraph of $\vec{G}$ is no longer a weakly $\mathcal{ST}$-reachable DAG. This DAG is a relaxed version of the original (or strongly) $\mathcal{ST}$-reachable DAG, where every target is reachable from every sender. This is because a strongly $\mathcal{ST}$-reachable DAG $G$ does not always exist; some graph has no strongly $\mathcal{ST}$-reachable DAG even in the case $|\mathcal{S}|=|\mathcal{T}|=2$. On the other hand, the proposed algorithm always constructs a weakly $\mathcal{ST}$-reachable DAG for any $|\mathcal{S}|$ and $|\mathcal{T}|$. Furthermore, the proposed algorithm is self-stabilizing; even if the constructed DAG deviates from the reachability requirement by a breakdown or exhausting the battery of a node having an arc in the DAG, this algorithm automatically reconstructs the DAG to satisfy the requirement again. The convergence time of the algorithm is $O(D)$ asynchronous rounds, where $D$ is the diameter of a given graph. We conduct small simulations to evaluate the performance of the proposed algorithm. The simulation result indicates that its execution time decreases when the number of sender nodes or target nodes is large.

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