Distributed algorithm for parallel computation of the n queens solutions

Abstract

The n-queen problem represents a classic challenge in artificial intelligence (AI) research. It involves the placement of n queens on an n x n chessboard, with the objective of ensuring that no queen threatens another. This problem has long been a source of fascination for mathematicians and computer scientists alike due to its inherent complexity. It is a well-known fact that as the value of ‘n’ increases, the problem becomes more challenging and falls into the NP problem class. Given the computational demands of the problem, parallel methods are of critical importance. It is noteworthy that scalable and parallel approaches for the n-queen problem remain to be developed. The majority of existing methods working on graphs attempt to parallelize a recursive sequential algorithm. However, the unpredictable nature of these algorithms makes it challenging to parallelize them on modern computer architectures. Consequently, we have selected an iterative algorithm from the literature in order to facilitate parallelization. This paper presents an innovative approach to parallelization that differs from traditional matrix-based strategies. The n-queen graph is distributed among a network of nodes, ensuring effective load balancing through dynamic partitioning and real-time computation. Our bespoke distributed algorithm, designed for the maximum clique problem on the n-queen graph, operates with true concurrency, thus obviating the necessity for resource or data sharing. The results of our assessment demonstrate that the parallel algorithm outperforms a cutting-edge sequential algorithm in terms of task completion time. The findings demonstrate that the speedups are almost perfect and that the workloads are distributed evenly across the network nodes. Furthermore, the results demonstrate high scalability, with task completion times decreasing as the number of nodes increases.