New Dynamic Programming Algorithm for the Multiobjective Minimum Spanning Tree Problem

TL;DR

This paper introduces a novel dynamic programming algorithm for the multiobjective minimum spanning tree problem, utilizing a transition graph and an improved Dijkstra-based method, outperforming existing algorithms on benchmark instances.

Contribution

The paper presents a new dynamic programming approach for MO-MST, including a size-reduction technique and an enhanced MOSP algorithm, advancing solution efficiency and scalability.

Findings

The new IG-MDA algorithm outperforms current state-of-the-art methods.

Cost-dependent arc pruning reduces the transition graph size.

The approach is validated on a large set of benchmark instances.

Abstract

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.