  We explore the use of remapping techniques to improve the efficiency of
highly-multiplexed fibre systems for astronomical spectroscopy. This is
particularly important for the implementation of Diverse Field Spectroscopy
(DFS, described in Paper II) using highly-multiplexed monolithic fibre systems
(MFS). Diverse Field Spectroscopy allows arbitrary distributions of target
regions to be addressed to optimise observing efficiency when observing
complex, clumpy structures such as protoclusters which will be increasingly
accessible to Extremely Large Telescopes (ELTS). We show how the adoption of
various types of remapping between the input and output of a Monolithic Fibre
Systems can allow contiguous regions of spatial elements to be selected using
only simple switch arrays. Finally we show how this compares in efficiency with
integral-field and multiobject spectroscopy by simulations using artificial and
real catalogues of objects. With the adoption of these mapping strategies, DFS
outperforms other techniques when addressing a range of realistic target
distributions. These techniques are also applicable to bio-medical science and
were in fact inspired by it.
