Parallel algorithms for the all nearest neighbors of binary image on the bulk-synchronous parallel model

In this paper, we present two parallel algorithms for computing the all nearest neighbors of an n × n binary image on the Bulk-Synchronous Parallel (BSP) model. The BSP model is an asynchronous parallel computing model, where its communication features are abstracted by two parameters L and g: L denotes synchronization periodicity and g denotes a reciprocal of communication bandwidth. We propose two parallel algorithms for the all nearest neighbor problems based on two distance metrics. The first algorithm is for Lp distance, and the second algorithm is for weighted distance. Both algorithms run in O[(n²/p) + L] computation time and in O[g(n/√(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[g (n/√(p)) + (gd + L) (log (p/n)/log(d+1))] communication time using p (n < p ≤ n²) processors on the BSP model, for any integer d (1 ≤ d ≤ p/n).