FAST MASSIVELY-PARALLEL ALGORITHMS FOR SHORTEST-PATH WITHIN PLANAR FIGURES

The problem of finding the shortest path between the given terminal po ints s and t within a given planar figure F is considered. The approac h contains basic methodology developed for any parallel or distributed system. The 2D scene or the edge of F are represented in the n Cartes ian coordinate system (n-CCS). Several algorithms for the shortest pat h are given, each one to be applied in specified circumstances dependi ng on the exact machine model or on additional information concerning geometrical properties of the figure. If these algorithms are implemen ted in a parallel depth search machine (PDSM), then the shortest path can be computed in time O(1). The maximum number of processors used is 0(n). The given methodology can also be adapted for producing an appr oximate solution when the shortest path is approximated by polygonal l ines.