  The Abstract Milling problem is a natural and quite general graph-theoretic
model for geometric milling problems. Given a graph, one asks for a walk that
covers all its vertices with a minimum number of turns, as specified in the
graph model by a 0/1 turncost function fx at each vertex x giving, for each
ordered pair of edges (e,f) incident at x, the turn cost at x of a walk that
enters the vertex on edge e and departs on edge f. We describe an initial study
of the parameterized complexity of the problem. Our main positive result shows
that Abstract Milling, parameterized by: number of turns, treewidth and maximum
degree, is fixed-parameter tractable, We also show that Abstract Milling
parameterized by (only) the number of turns and the pathwidth, is hard for W[1]
-- one of the few parameterized intractability results for bounded pathwidth.
