| Summary: | In this thesis we present an optimal linear time algorithm for validating the correctness of a map by an active agent (such as a person or a mobile robot). The robot is given a possibly incorrect map (model) of its environment. This model GM is given as an embedding of an undirected planar graph without edge crossings. The correct model GW of the environment, referred to as the underlying real world GW, is unknown to the robot. The underlying real world GW is an embedding of an arbitrary, not necessarily planar, graph. The robot begins at some arbitrary location in GM; this initial location is known to the robot. The robot must determine whether its map GM is consistent with the real world GW with respect to the given initial position. === The robot is assumed to be able to autonomously traverse graph edges, recognize when it has reached a vertex, and locally order edges incident upon the current vertex. The robot cannot measure distances nor does it have a compass, but it is equipped with a single marker that it can leave at a vertex and sense its presence. In addition to the linear plane graph validation algorithm, we present an approach to solve the problem efficiently for some non-planar embeddings. Namely, if the given map GM is a non-planar embedding of a combinatorially planar graph, we can solve this problem with a similar approach such that the complexity remains linear.
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