  The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the
Minimum Spanning Tree problem, in which the costs associated with every edge of
the input graph are vectors. In this paper, we design a new dynamic programming
MO-MST algorithm. Dynamic programming for a MO-MST instance leads to the
definition of an instance of the One-to-One Multiobjective Shortest Path (MOSP)
problem and both instances have equivalent solution sets. The arising MOSP
instance is defined on a so called transition graph. We study the original size
of this graph in detail and reduce its size using cost dependent arc pruning
criteria. To solve the MOSP instance on the reduced transition graph, we design
the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting
recent improvements on MOSP algorithms from the literature. All in all, the new
IG-MDA outperforms the current state of the art on a big set of instances from
the literature. Our code and results are publicly available.
