Network contamination & graphs

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Graph searching models often use the metaphor of decontaminating a network. For example, consider a network of pipes with a regenerating biological contaminant that is mobile so that contamination can spread from one area to another. Mobile agents are used to clean the network. Of particular interest in this proposal is the situation where the network has to be cleaned regularly because of a slow growing contaminant, such as algae or zebra mussels. My goals are to analyze these graph searching and cleaning models and establish relationships to other problems and applications.