Parallel implementations of discrete relaxation technique on fixed size processor arrays

Discrete relaxation technique has been widely used in pattern recognition, artificial intelligence and computer vision. For the consistent labeling problem for labeling n objects with m labels, a parallel implementation based on a new sequential algorithm is shown. This non-partitioned parallel implementation runs in O(nm) time using nm PE´s. Two partitioned implementations are then proposed. In the first implementation, O(n²m²/ P) time performance is achieved by using P PE´s connected to a common bus, where P⩽nm. An alternate linear array implementation is also proposed which runs in O((nm/P+P)nm) time. This achieves linear speedup when nm⩾P²