Parallel algorithms for all nearest neighbors of binary images on the BSP model

We present two parallel algorithms for computing the nearest neighbors of an n×n binary image on the Bulk-Synchronous Parallel (BSP) model. The first algorithm is for weighted distance, and the second algorithm is for L_p distance. Both algorithms run in O(n²/p+L) computation time and O(gⁿ/√p+L) communication time using p (1⩽p⩽n) processors and in O(n² /p+(d+L)log p/n/log(d+1)) computation time and in O(gn/√p+(gd+L)log p/n/log(d+1)) communication time using p (n<p⩽n²) processors, for any integer d (1⩽d⩽p/n), where L denotes synchronization periodicity and g denotes a reciprocal of communication bandwidth