Constant Time Collision-Free Path Computation on Reconfigurable Mesh

The reconfigurable mesh (R-Mesh) was shown to be a very powerful model capable of extremely fast solutions to many problems. R-Mesh has a wide range of applications such as arithmetic problems, image processing and robotics. The 2D R-Mesh was shown to be able to solve the path planning problem very fast. In this paper, we propose an algorithm to compute a collision-free path between a source and a destination in an environment with the existence of obstacles. Independent of the number of obstacles, k, the proposed algorithm runs in constant time and requires O(log 2 N) pre-processing time where N is the size of the R-Mesh. This is in contrast to the previous work that requires O(k) time with the same preprocessing time. We then make a modification to the obtained path to enhance its length. This enhancement also requires constant time. Keywords-parallel algorithms, reconfigurable mesh, path planning