Accelerating the Dynamic Programming for the Optimal Polygon Triangulation on the GPU

Modern GPUs (Graphics Processing Units) can be used for general purpose parallel computation. Users can develop parallel programs running on GPUs using programming architecture called CUDA (Compute Unified Device Architecture). The optimal polygon triangulation problem for a convex polygon is an optimization problem to find a triangulation with minimum total weight. It is known that this problem can be solved using the dynamic programming technique in

O

(

n

3

) time using a work space of size

O

(

n

2

). The main contribution of this paper is to present an efficient parallel implementation of this

O

(

n

3

)-time algorithm on the GPU. In our implementation, we have used two new ideas to accelerate the dynamic programming. The first idea (granularity adjustment) is to partition the dynamic programming algorithm into many sequential kernel calls of CUDA, and to select the best size and number of blocks and threads for each kernel call. The second idea (sliding and mirroring arrangements) is to arrange the temporary data for coalesced access of the global memory in the GPU to minimize the memory access overhead. Our implementation using these two ideas solves the optimal polygon triangulation problem for a convex 16384-gon in 69.1 seconds on the NVIDIA GeForce GTX 580, while a conventional CPU implementation runs in 17105.5 seconds. Thus, our GPU implementation attains a speedup factor of 247.5.