Navigation for a team of agents is a challenging but interesting problem with a variety of applications, including fleet operations in warehouses, video games, and drone shows. In this talk, I provide an overview of techniques for controlling multiple moving agents. The talk includes multi-agent pathfinding (MAPF) which aims at finding a set of collision-free paths on graphs, planning in continuous spaces, and robust execution policies for real robots.

To evaluate the fittings of statistical models on finite discrete spaces, we consider Monte Carlo simulation methods using Markov chain. To construct a connected Markov chain on a given space, we consider a Markov basis, which is characterized algebraically and is calculated by the theory of Groebner basis of the polynomial rings. In this talk, I give some primers on statistics and algebra to understand this topic, with some related works.

Enumerating subgraphs of a given graph is a fundamental task in computer science. Since the number of subgraphs can be exponentially larger than the input graph size, it is not practical to list all subgraphs one by one. To overcome the difficulty, we focus on implicit enumeration algorithms. Such an algorithm constructs a decision diagram (DD) representing the set of subgraphs instead of explicitly enumerating the subgraphs. In this talk, we introduce recent studies on implicit subgraph enumeration using DDs.

A distributed system is a system of autonomous computing entities, that communicate and cooperate with each other. Each computing entity does not know the global system configuration, and locally performs computation and communication in parallel. This talk first presents a short survey on recent results on distributed reconfiguration problems on a communication graph of a distributed system, for example, independent sets [ICALP2019], vertex colorings [DISC2018], and spanning trees [SSS 2021]. These papers consider different difficulties in distributed computing. Then, the talk proceeds to reconfiguration in distributed systems of autonomous mobile computing entities, such as mobile robots and agents. Reconfiguration in such distributed systems have been considered for geometric positions of computing entities and called the pattern formation problem and distributed reconfiguration. The speaker recently works on solving problem such as search and evacuation by combinations of reconfiguration sequences. The talk addresses pattern formation by mobile robots and search and evacuation by a metamorphic robotic system.

In this talk, I consider a matching in a bipartite graph in which each vertex has a preference over the edges incident to it. Especially, I focus on a Pareto stable matching, which is a matching satisfying stability and Pareto efficiency. In talk, I give a survey of a Pareto stable matching including my recent result. I also talk about the relationship between Pareto stable matchings and combinatorial reconfiguration.