On the Eeciency of Parallel Backtracking

It is known that isolated executions of parallel backtrack search exhibit speedup anomalies. In this paper we present analytical models and experimental results on the average case behavior of parallel backtracking. We consider two types of backtrack search algorithms: (i) simple backtracking (which does not use any heuristic information); (ii) heuristic backtracking (which uses heuristics to order and prune search). We present analytical models to compare the average number of nodes visited in sequential and parallel search for each case. For simple backtracking, we show that the average speedup obtained is (i) linear when distribution of solutions is uniform and (ii) super-linear when distribution of solutions is non-uniform. For heuristic backtracking, the average speedup obtained is at least linear (i.e., either linear or superlinear), and the speedup obtained on a subset of instances (called diicult instances) is superlinear. We also present experimental results over many synthetic and practical problems on various parallel machines, that validate our theoretical analysis.