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William McLendon, Bruce Hendrickson, Steve Plimpton, Lawrence Rauchwerger, "Finding Strongly Connected Components in Parallel in Particle Transport Sweeps," In Proc. ACM Symp. Par. Alg. Arch. (SPAA), pp. 328-329, Crete, Greece, Jul 2001.
Proceedings(ps, pdf, abstract)

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.