Cleaning a graph

Suppose there is a network of pipes with a slow growing `contaminant', such as algae. Brushes can traverse an edge thereby cleaning it. What are efficient method for continually cleaning the network? In the talk I will survey some of the types of problems and solutions that we have found and mention some of the open problems. This is joint work with Margaret-Ellen Messinger (Ph.D. candidate) and Dr Pawel Pralat.