Path planning on a ring of processors∗∗

Abstract

In this paper, we discuss the implementation of Bitz and Kung's path planning algorithm on a ring of general-purpose 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 inter-processor communications that it requires. We design a modified version that is much more performing. 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) = (l, 1). 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.