Efficient algorithms for discrete lattice calculations

We discuss algorithms for lattice-based computations, in particular lattice reduction, the detection of nearest neighbors, and the computation of clusters of nearest neighbors. We focus on algorithms that are most efficient for low spatial dimensions (typically d=2,3$d=2\text{,}3$) and input data within a reasonably limited range. This makes them most useful for physically oriented numerical simulations, for example of crystalline solids. Different solution strategies are discussed, formulated as algorithms, and numerically evaluated.