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Lattice template placement for coherent all-sky searches for gravitational-wave pulsars

All-sky, broadband, coherent searches for gravitational-wave pulsars are restricted by limited computational resources. Minimizing the number of templates required to cover the search parameter space, of sky position and frequency evolution, is one important way to reduce the computational cost of a search. We demonstrate a practical algorithm which, for the first time, achieves template placement with a minimal number of templates for an all-sky search, using the reduced supersky parameter-space metric of Wette and Prix [Phys. Rev. D 88, 123005 (2013)]. The metric prescribes a constant template density in the signal parameters, which permits that templates be placed at the vertices of a lattice. We demonstrate how to ensure complete coverage of the parameter space, including in particular at its boundaries. The number of templates generated by the algorithm is compared to theoretical estimates, and to previous predictions by Brady et al. [Phys. Rev. D 57, 2101 (1998)]. The algorithm may be applied to any search parameter space with a constant template density, which includes semicoherent searches and searches targeting known low-mass X-ray binaries.