Optimal orderings of k-subsets for star identification

Finding the optimal ordering of k-subsets with respect to an objective function is known to be an extremely challenging problem. In this paper we introduce a new objective for this task, rooted in the problem of star identification on spacecrafts: subsets of detected spikes are to be generated in an ordering that minimizes time to detection of a valid star constellation. We carry out an extensive analysis of the combinatorial optimization problem, and propose multiple algorithmic solutions, offering different quality-complexity trade-offs. Three main approaches are investigated: exhaustive search (branch and prune), goal-driven (greedy scene elimination, minimally intersecting subsets), and stateless algorithms which implicitly seek to satisfy the problem's goals (pattern shifting, base unrank). In practical terms, these last algorithms are found to provide satisfactory approximations to the ideal performance levels, at small computational costs.