The algebraic path problem (APP) unifies a number of related combinatorial or numerical problems into one that can be resolved by a generic algorithmic schema. In this paper, we propose a linear SPMD model based on the Warshall-Floyd procedure with a shift-toröıdal postprocessing at each step to solve the problem in a work optimal manner. The initial solution requires a number of nodes that equals the size of the input matrix. With a fewer number of computing nodes, we exploit the modularity revealed by our scheduling to achieve the task using a locally parallel and globally sequential (LPGS) partitioning. Moreover, our solution requires a fewer local memory on each node. These two characteristics motivate an implementation on the CELL processor, in addition to the efficient SPE to SPE communication bandwidth and the intrinsic power of each SPE. We report our experimentations on a QS22 CELL blade on various input configurations and exhibit the efficiency and scalability of our implementation.