Load Balancing and Parallel Tree Search: The MPIDA• Algorithm

This paper presents a parallel implementation of the Iterative-Deepening A* algorithm on a parallel distributed memory machine. Two kinds of dynamic load balancing strategies have been studied to overcome the irregular tree search problem. To study the eeectiveness of the algorithm, it has been tested to solve a NP-complete problem: the fteen puzzle. Our experimental results on a cluster of 16 ALPHA processors using PVM show that an eeciency of 97.54% for a speedup of 15.61 could be achieved on a hard problem. 1. Motivation Time complexity of tree search algorithms is considerably reduced by the use of a heuristic function that estimates the cost of reaching a solution from a given state. Many algorithms were described in the literature (A*, IDA*, Branch and bound, ...). The exponential memory requirement of A* is overcome by IDA* algorithm 1] among others (MA**2], MRECC3], PRA**4], ...). IDA* works by performing a series of iterations. In each iteration, IDA* performs a depth-rst search from the initial state while the cost of the nodes don't exceed a xed threshold. If no solution is found, IDA* increases the threshold and goes on a new iteration as described before. The total cost f of the current node is composed of the cost g of reaching the current node plus the estimated cost h of the path from the current node to a goal state. At the start point the threshold is the estimate cost of the initial state and then it increases to the minimum cost of frontier nodes in the previous iteration. Under some conditions on the heuristic function f (admis-sibility and monotonicity 1]), the solution found by IDA* is guaranteed to be optimal. Although IDA* is optimal in terms of solution cost and space over the class of admissible best rst searches, some problems still need huge computation time. This motivates the use of parallel processing. Diierent approaches can be used to parallelize tree search algorithms 5]. Our parallel implementation MPIDA*, which stands for Message Passing IDA*, uses tree decomposition: the tree search is divided into subtrees which are assigned to diierent processors and each processor performs the same search algorithm on its own subtree (SPMD model). This approach is quite simple and independant of the problem. Because subtrees associated to each processor are irregular, the speedup provided by the parallelization on its own is insuucient, so that load balancing is required to redistribute …