Computational issues in systems of mobile entities

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In this project I am interested in the design of deterministic algorithms for groups of computational moving entities. Such entities are identical, extremely simple and individually quite weak; but collectively capable of performing possibly complex tasks. The environment in which the entities operate can be a network or a terrain. In both environments the behaviour of the entities is cyclic: an entity becomes active (asynchronously and independently), it decides where to move based on the protocol, it moves to a location, and it becomes inactive again. What can be done by a team of entities and how efficiently depends on the characteristics of the entities like, for example, their communication media, their ability to see neighbouring entities, their level of synchronization, the possibility to remember the past. Some of the entities' characteristics (for example, locality, obliviousness, and communication) are particularly important and their study could have significant consequences in terms of scalability, efficiency, and fault-tolerance. The main objective of the project is to study the above mentioned characteristics to understand the extent of their impact on typical coordination problems. In particular, I will focus on identifying the minimal capabilities that allows the entities to successfully perform their tasks. The main novelty of my approach is to tackle the various problems (e.g., pattern formation, exploration, rendezvous, flocking) from an analytical and deterministic standpoint as opposed to following probabilistic approaches or empirical methods. The approach I will follow is typical to the fields of algorithms and theoretical computer science and will consist of first creating coherent and precise models of the problems under investigation, secondly solving problems or identifying situations of unsolvability. The algorithmic solutions will employ a variety of techniques based on combinatorics, discrete mathematics, graph theory, and geometry. The significant consequences of this study will be a better understanding of the computational power of mobile computational entities and the design of novel algorithms that are scalable, fault-tolerant, and possibly self-stabilizing.