Fast algorithms for a space-time concordance measure

This paper presents a number of algorithms for a recently developed measure of space-time concordance. Based on a spatially explicit version of Kendall's τ the original implementation of the concordance measure relied on a brute force O(n²) algorithm which has limited its use to modest sized problems. Several new algorithms have been devised which move this run time to O(n log(n) +np) where p is the expected number of spatial neighbors for each unit. Comparative timing of these alternative implementations reveals dramatic efficiency gains in moving away from the brute force algorithms. A tree-based implementation of the spatial concordance is also found to dominate a merge sort implementation.