  We consider problems in which a simple path of fixed length, in an undirected
graph, is to be shifted from a start position to a goal position by moves that
add an edge to either end of the path and remove an edge from the other end. We
show that this problem may be solved in linear time in trees, and is
fixed-parameter tractable when parameterized either by the cyclomatic number of
the input graph or by the length of the path. However, it is PSPACE-complete
for paths of unbounded length in graphs of bounded bandwidth.
