  The proposed designs of many auxiliary long-lived particle (LLP) detectors at
the LHC call for the instrumentation of a large surface area inside the
detector volume, in order to reliably reconstruct tracks and LLP decay
vertices. Taking the CODEX-b detector as an example, we provide a
proof-of-concept optimization analysis that demonstrates the required
instrumented surface area can be substantially reduced for many LLP models,
while only marginally affecting the LLP signal efficiency. This optimization
permits a significant reduction in cost and installation time, and may also
inform the installation order for modular detector elements. We derive a
branch-and-bound based optimization algorithm that permits highly
computationally efficient determination of optimal detector configurations,
subject to any specified LLP vertex and track reconstruction requirements. We
outline the features of a newly-developed generalized simulation framework, for
the computation of LLP signal efficiencies across a range of LLP models and
detector geometries.
