New Anticipatory Load Balancing Strategies for Parallel A* Algorithms

In this paper, we develop load balancing strategies for scalable high-performance parallel A* algorithms suitable for distributed-memory machines. In parallel A* search, ineeciencies such as processor starvation and search of non-essential spaces (search spaces not explored by the sequential algorithm) grow with the number of processors P used, thus restricting its scalability. To alleviate this eeect, we propose a novel parallel startup phase and an eecient dynamic load balancing strategy called the quality equalizing (QE) strategy. Our new parallel startup scheme executes optimally in (logP) time and, in addition, achieves good initial load balance. The QE strategy employs near-neighbor quantitative and qualitative load balancing schemes to achieve load balance. These schemes utilize anticipatory mechanisms to detect and correct load imbalance before its actual occurrence; such mechanisms are particularly useful at lower work densities (the ratio of the problem size to P) and for lower granularity applications. The QE strategy possesses certain unique load balancing properties that enable it to signiicantly reduce starvation and non-essential work, and that make its performance robust across applications with diierent cost distributions for search-space nodes. Consequently, we obtain a highly scalable parallel A* algorithm with an almost-linear speedup. The startup and load balancing schemes were employed in parallel A* algorithms to solve the Traveling Salesman Problem on an nCUBE2 hypercube multicomputer. The QE strategy yields average speedup improvements of about 20-185% and 15-120% at low and intermediate work densities, respectively, over three well-known load balancing methods|the round-robin (RR), the random communication (RC) and the neighborhood averaging (NA) strategies. The average speedup observed on 1024 processors is about 985, representing a very high eeciency of 0:96. We also tested the eeect of including an anticipatory qualitative load balancing scheme in the QE strategy and found that it reduces the average execution time by 3:32% and 8:77% on 1 256 and 512 processors, respectively, at lower work densities. Finally, we present analytical and empirical results on the scalability of parallel A* algorithms in terms of the isoeeciency metric. Our analytical results include (1) a (P: log P) lower bound on the isoeeciency function of any parallel A* algorithm, and (2) a general expression for the upper bound on the isoeeciency function of our parallel A* algorithm using the QE strategy on any topology|for the hypercube and 2-D mesh ar-chitectures the upper bounds on the isoeeciency function are found to be (P: log 2 P) and (P: p …