Path Planning on a Distributed Memory Computer

In this paper, we discuss the implementation of Bitz and Kungs path planning algorithm on a ring of generalpurpose processors. We show that Bitz and Kung's algorithm, originally designed for the Warp machine, is not efficient in this context, due to the intensive interprocessor communications that it requires. We design a modified version that performs much better. The new version updates a segment of k positions within a step and allocates blocks of r consecutive rows of the map to the processors in a wraparound fashion. Bitz and Kung's algorithm corresponds to the situation (k,r) = (I ,I). We analytically determine the optimal values of the parameters (k,r) which minimize the parallel execution time as a function of the problem size n and of the number of processors p. The theoretical results are nicely corroborated by numerical experiments on a ring of 32 Transputers. Kung's algorithm is not efficient in the context of general purpose processors, due to the intensive communication scheme that it requires.