Bitwise-Parallel Reduction for Connection Tests

Abstract

This paper introduces bitwise-parallel reduction (BPR), an efficient method for performing connection tests in hexagonal connection games such as Hex and Y. BPR is based on a known property of Y that games can be reduced to a single value indicating the fully connected player (if any) through a sequence of reduction operations. We adapt this process for bitwise-parallel implementation and demonstrate its benefit over a range of board sizes. BPR is by far the fastest known method if connection tests only need to be performed once per game, for example, to evaluate board fills following Monte Carlo playouts.