On the efficiency of parallel backtracking

Analytical models and experimental results concerning the average case behavior of parallel backtracking are presented. Two types of backtrack search algorithms are considered: simple backtracking, which does not use heuristics to order and prune search, and heuristic backtracking, which does. Analytical models are used to compare the average number of nodes visited in sequential and parallel search for each case. For simple backtracking, it is shown that the average speedup obtained is linear when the distribution of solutions is uniform and superlinear when the distribution of solutions is nonuniform. For heuristic backtracking, the average speedup obtained is at least linear, and the speedup obtained on a subset of instances is superlinear. Experimental results for many synthetic and practical problems run on various parallel machines that validate the theoretical analysis are presented