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.

翻译：多目标最小生成树（MO-MST）问题是最小生成树问题的一个变体，其中输入图中每条边关联的成本均为向量。本文设计了一种新的动态规划MO-MST算法。针对MO-MST实例的动态规划过程会对应定义一个一对一多目标最短路径（MOSP）问题实例，且这两个实例具有等价的解集。所生成的MOSP实例定义在所谓的转移图上。我们详细研究了该图的原始规模，并利用基于成本相关的弧剪枝准则对其规模进行缩减。为求解缩减后转移图上的MOSP实例，我们设计了隐式图多目标Dijkstra算法（IG-MDA），该算法充分利用了文献中MOSP算法的最新改进。总体而言，新提出的IG-MDA在文献中的大规模实例集上优于当前最先进方法。我们的代码与结果已公开。