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The efficient placement of signal templates in source-parameter space is acrucial requisite for exhaustive matched-filtering searches of modeledgravitational-wave sources. Unfortunately, the current placement algorithmsbased on regular parameter-space meshes are difficult to generalize beyondsimple signal models with few parameters. Various authors have suggested that ageneral, flexible, yet efficient alternative can be found in randomizedplacement strategies such as random placement and stochastic placement, whichenhances random placement by selectively rejecting templates that are too closeto others. In this article we explore several theoretical and practical issuesin randomized placement: the size and performance of the resulting templatebanks; the effects of parameter-space boundaries; the use of quasi-random (selfavoiding) number sequences; most important, the implementation of thesealgorithms in curved signal manifolds with and without the use of a Riemanniansignal metric, which may be difficult to obtain. Specifically, we show how themetric can be replaced with a discrete triangulation-based representation oflocal geometry. We argue that the broad class of randomized placementalgorithms offers a promising answer to many search problems, but that thespecific choice of a scheme and its implementation details will still need tobe fine-tuned separately for each problem.

Cover art: issues in the metric-guided and metric-less placement of random and stochastic template banks