Extremal properties of flood-filling games

The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required, taken over all possible colourings. We give several upper and lower bounds on this quantity for arbitrary graphs and show that all of the bounds are tight for trees; we also investigate how much the upper bounds can be improved if we restrict our attention to graphs with higher edge-density.Comment: Final version, accepted to DMTC

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Topologic Maps for Robotic Exploration of Underground Flooded Mines

The mapping of confined environments in mobile robotics is traditionally tackled in dense occupancy maps, requiring large amounts of storage. For some use cases, such as the exploration of flooded mines, the use of dense maps in processing slow down processes like path generation. I introduce a method of generating topological maps in constrained spaces such as mines. By taking a structure with fewer points, traversal and storage of explored space can be made more efficient, avoiding com plex graphs generated by methods like RRT and it’s variants. It’s simpler structure also allows for more intuitive human-machine interactions with it’s fewer points. I also introduce an autonomous frontier-based exploration approach to generate the topological map during exploration, taking advantage of it’s traversal to navigate through known space. With this work, simulation tests show it is possible to success fully extract a simpler graph structure describing the topology during autonomous exploration and that this structure is robust through explored regionsO mapeamento de ambientes confinados em robótica móvel, é tradicionalmente abordado em mapas densos de ocupação, necessitando de grandes quantidades de armazenamento. Para certos casos, tal como a exploração de minas submersas, o uso de mapas densos no processamento, atrasa processos como geração de caminhos. Utilizando uma estrutura com menos pontos, a travessia e o armazenamento de espaço explorado tornam-se mais eficientes, evitando grafos complexos gerados por métodos como RRT e variantes. A sua estrutura mais simples permite também interações homem-máquina com o seu número reduzido de pontos. Introduzo também uma abordagem autónoma de exploração baseada em fronteiras, para gerar o mapa topo lógico durante a exploração, tirando vantagem da travessia do mesmo para navegar por espaço conhecido. Com este trabalho, testes em simulação mostram ser possível extrair uma estrutura sob forma de grafo, descrevendo a topologia ao longo de explorações autónomas e que esta estrutura é robusta para a travessia em regiões explorada

A Web Gaming Facility for Research and Teaching

This essay considers the potential for utilizing web games for research and teaching. It discusses a specific gaming facility that has been constructed and utilized. The gaming facility can be made available for use for those interested in utilizing it for teaching and/or research purposes. The goal is to have this facility be of use for both single play and repeated matrix games. Much of the discussion here is aimed at single play games as a desirable benchmark preliminary to the study of repeated games. Properties of the one stage games are discussed and instructions for the use of the system are supplied. Extensions to multistage games and incomplete information are noted

A Web Gaming Facility for Research and Teaching

This essay considers the potential for utilizing web games for research and teaching. It discusses a specific gaming facility that has been constructed and utilized. The gaming facility can be made available for use for those interested in utilizing it for teaching and/or research purposes. The goal is to have this facility be of use for both single play and repeated matrix games. Much of the discussion here is aimed at single play games as a desirable benchmark preliminary to the study of repeated games. Properties of the one stage games are discussed and instructions for the use of the system are supplied. Extensions to multistage games and incomplete information are noted

The Communication Complexity of Fault-Tolerant Distributed Computation of Aggregate Functions

Ph.DDOCTOR OF PHILOSOPH