Parallel Cluster Identiication for Multidimensional Lattices

The cluster identiication problem is a variant of connected component labeling that arises in cluster algorithms for spin models in statistical physics. We present a multidimensional version of Belkhale and Banerjee's Quad algorithm for connected component labeling on distributed memory parallel computers. Our extension abstracts away extraneous spatial con-nectivity information in more than two dimensions, simplifying implementation for higher di-mensionality. We identify two types of locality present in cluster conngurations, and present optimizations to exploit locality for better performance. Performance results from 2D, 3D, and 4D Ising model simulations with Swendson-Wang dynamics show that the optimizations improve performance by 20-80%.