Probabilistic fibre-to-target assignment algorithm for multi-object
  spectroscopic surveys
  Context. Several new multi-object spectrographs are currently planned or
under construction that are capable of observing thousands of Galactic and
extragalactic objects simultaneously.
  Aims. In this paper we present a probabilistic fibre-to-target assignment
algorithm that takes spectrograph targeting constraints into account and is
capable of dealing with multiple concurrent surveys. We present this algorithm
using the 4-metre Multi-Object Spectroscopic Telescope (4MOST) as an example.
  Methods. The key idea of the proposed algorithm is to assign probabilities to
fibre-target pairs. The assignment of probabilities takes the fibre
positioner's capabilities and constraints into account. Additionally, these
probabilities include requirements from surveys and take the required exposure
time, number density variation, and angular clustering of targets across each
survey into account. The main advantage of a probabilistic approach is that it
allows for accurate and easy computation of the target selection function for
the different surveys, which involves determining the probability of observing
a target, given an input catalogue.
  Results. The probabilistic fibre-to-target assignment allows us to achieve
maximally uniform completeness within a single field of view. The proposed
algorithm maximises the fraction of successfully observed targets whilst
minimising the selection bias as a function of exposure time. In the case of
several concurrent surveys, the algorithm maximally satisfies the scientific
requirements of each survey and no specific survey is penalised or prioritised.
  Conclusions. The algorithm presented is a proposed solution for the 4MOST
project that allows for an unbiased targeting of many simultaneous surveys.
With some modifications, the algorithm may also be applied to other
multi-object spectroscopic surveys.
