Discrete ordinates methods are commonly used to simulate radiation transport for fire or weapons modeling. The computation proceeds by sweeping the flux across a grid. A particular cell cannot be computed until all the cells immediately upwind of it are finished. If the directed dependence graph for the grid cells contains a cycle then sweeping methods will deadlock. This can happen in unstructured grids and time stepped problems where the grid is allowed to deform. In this paper we present a parallel algorithm to detect cycles in the dependence graphs present in these grids as well as an implementation and experimental results on shared and distributed memory machines.