Yuichi Sudo

Yuichi Sudo

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, Gąsieniec, 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 $2^{O(n^ρ\log n)}$-state SS-LE protocol with a parameter $ρ$: setting $ρ= Θ(\log n)$ yields an optimal $O(\log n)$ time both in expectation and w.h.p., while $ρ= Θ(1)$ results in $O(ρ\,n^{1/(ρ+1)})$ expected time. Recently, Austin, Berenbrink, Friedetzky, Götte, and Hintze [ABF+25] (PODC) presented a novel SS-LE protocol parameterized by a positive integer $ρ$ with $1 \le ρ< n/2$ that solves SS-LE in $O(\frac{n}ρ\cdot\log n)$ time w.h.p.\ using $2^{O(ρ^2\log n)}$ states. This paper independently presents yet another time--space tradeoff of SS-LE: for any positive integer $ρ$ with $2 \le ρ\le \sqrt{n}$, SS-LE can be achieved within $O\left(\frac{n}ρ\cdot \logρ\right)$ expected time using $2^{2ρ\lg^2ρ+ O(\log n)}$ states. The proposed protocol uses significantly fewer states than [ABF+25] for any expected stabilization time above $Θ(\sqrt{n}\log n)$. When $ρ= Θ\left(\frac{\log n}{\log^2 \log n}\right)$, 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 $ρ\le\sqrt{n}$ prevents achieving $o(\sqrt{n}\log n)$ time, whereas the protocol of [ABF+25] can surpass this bound.

Yuichi Sudo, Naoki Kitamura, Masahiro Shibata et al.

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 $T = Ω(m)$ is necessary. We also present deterministic algorithms whose required window size is $O(ε(n,m)\cdot m + n \log^2 n)$, where $ε(n,m) = \frac{\ln n}{1 + \ln m - \ln n}$. These bounds are tight for a wide range of $m$, in particular when $m = n^{1+Θ(1)}$. The same algorithms also yield optimal or near-optimal exploration time: we prove lower bounds of $Ω((m - n + 1)n)$ in the $KT_0$ model and $Ω(m)$ in the $KT_1$ model, and show that our algorithms match these bounds up to a polylogarithmic factor, while being fully time-optimal when $m = n^{1+Θ(1)}$. This yields tight bounds when parameterized solely by $n$: $Θ(n^3)$ for $KT_0$ and $Θ(n^2)$ for $KT_1$.

Masahiro Shibata, Masaki Ohyabu, Yuichi Sudo et al.

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.