Random template banks and relaxed lattice coverings

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The traditional approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability eta < 1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are random template banks in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study relaxed lattice coverings (using Z(n) and A(n)(*) lattices), which similarly cover any signal location only with probability eta. The relaxed A(n)(*) lattice is found to yield the most efficient template banks at low dimensions (n less than or similar to 10), while random template banks increasingly outperform any other method at higher dimensions.