Algorithms for Mobile Agents with Limited Capabilities

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This work deals with geometric problems and the use of limited capability agents for these problems. Exploration and guarding problems have been extensively studied in computational geometry. The basic task is to monitor an environment (a polygon) either with a mobile guard or with a number of sta¬tionary guards (or guards with hard restrictions on the allowed movements). Though all these problems are easy to formulate-and have real-world interpretations that vividly illustrate them-some of these problems (as the classical art gallery problem) are hard to solve. The task of exploring an environment becomes more challenging if the environment is not known in advance, that is, there is no given ground plan and only areas that have already been visibly encountered by the explorer are known. Problems with this kind of uncertainty are called online problems. For o¿ine problems the ground plan of the environment is known in advance. In this work we study one o¿ine exploration problem and one exploration and guarding problem in the o¿ine and online version, where the focus is on the latter. For our problems we do not deal with "almighty" explorers, but face limits on their perceptive capabilities. Other types of geometric problems can exploit this kind of limited agents: We present an exact and fast algorithm for an image analysis task with polyomino-shaped objects on a grid.