In this paper, we consider the pattern formation problem of mobile agents in n×m dynamic grids, requiring k agents in the grid to stay at x designated(target) nodes to form some shape (pattern). We assume that at most one link is missing at each round. In this case, some agent’s movement may be always blocked and the agent cannot reach any target node. In addition, if the number k of agents is smaller than the number x of target nodes, several target nodes cannot be occupied. For this reason, focusing on the relationship between the values of k and x, we consider variants of the pattern formation problem in dynamic grids and examine how differences in these requirements and the number of agents influence the design and performance of algorithms. First, we consider the case of k≤x. In this case, we consider the approximate pattern formation problem, requiring at least k-1(x. In this case, we consider the exact pattern formation problem, requiring each of the x target nodes to be occupied. For this problem, we propose an algorithm to achieve exact pattern formation in O(kn+km+mn) rounds. In particular, when k-x is sufficiently large, we show that exact pattern formation can be achieved in Θ(n+m) rounds. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

In a network (graph) G = (V,E), a set S ⫅ V of processes is a total dominating set if every process is neighboring to some member of S. This paper considers the dynamic total domination problem, a new process synchronization problem in distributed systems. It dynamically maintains a total dominating set. Each process in the total dominating set is in its critical section (CS). That is, the problem is controlling the system in such a way that, for each process, at least one neighboring process must be in the CS at each time. This problem has an interesting application, such as an environmental monitoring IoT system with rechargeable batteries. In this paper, we propose a self-stabilizing distributed algorithm for the dynamic total domination problem under a weakly fair distributed daemon. © 2025 IEEE.

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 Kn,n, which consists of two n-node sets VL and VR, the uniform deployment problem requires the robots to achieve one of the following configurations: (a) each node in VL is occupied by exactly one robot, with no robots in VR, or (b) each node in VR is occupied by exactly one robot, with no robots in VL. 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. © Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, Yonghwan Kim, Yoshiaki Katayama, Toshimitsu Masuzawa, Quentin Bramas, and Sébastien Tixeuil;