  We classify the thick subcategories of discrete derived categories. To do
this we introduce certain generating sets called arc-collections which
correspond to configurations of non-crossing arcs on a geometric model. We show
that every thick subcategory is generated by an arc-collection, each thick
subcategory is determined by the topology of the corresponding configuration,
and we describe a version of mutation which acts transitively on the set of
arc-collections generating a given thick subcategory.
