  Solving the Lexicographic Bottleneck Assignment Problem (LexBAP) typically
relies on centralised computation with order quartic complexity. We consider
the Sequential Bottleneck Assignment Problem (SeqBAP), which yields a greedy
solution to the LexBAP and discuss the relationship between the SeqBAP, the
LexBAP, and the Bottleneck Assignment Problem (BAP). In particular, we
reexamine tools used to analyse the structure of the BAP, and apply them to
derive an algorithm that solves the SeqBAP with cubic complexity. We show that
the set of solutions of the LexBAP is a subset of the solutions of the SeqBAP
and analyse the conditions for which the solutions sets are identical.
Furthermore, we provide a method to verify the satisfaction of these
conditions. In cases where the conditions are satisfied, the proposed algorithm
for solving the SeqBAP solves the LexBAP with computation that has lower
complexity and can be distributed over a network of computing agents. The
applicability of the approach is demonstrated with a case study where mobile
robots are assigned to goal locations.
