Mejora de la exploracion y la explotacion de las heuristicas constructivas para el MLSTP

TL;DR

This paper investigates constructive heuristics for the NP-complete minimum labeling spanning tree problem, aiming to find spanning trees with minimal label diversity, and compares different heuristic variants to improve efficiency.

Contribution

It introduces and compares several variants of a primary heuristic for the MLST problem, enhancing understanding of their efficiency improvements.

Findings

The maximum vertex covering heuristic is effective for MLST.

Variants of the heuristic show improved efficiency in different scenarios.

The problem remains NP-complete even for complete graphs.

Abstract

This paper studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge), the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest possible number of distinct labels. The model can represent many real-world problems in telecommunication networks, electric networks, and multimodal transportation networks, among others, and the problem has been shown to be NP-complete even for complete graphs. A primary heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of this constructive heuristic have been proposed to improve its efficiency. Here we describe the problem, review the literature and compare some variants of this algorithm.