Local search for the minimum label spanning tree problem with bounded color classes

Local search for the minimum label spanning tree problem with bounded color classes

In the Minimum Label Spanning Tree problem, the input consists of an edge-colored undirected graph, and the goal is to find a spanning tree with the minimum number of different colors. We investigate the special case where every color appears at most r times in the input graph. This special case is polynomially solvable for r = 2, and NP-complete and APX-complete for any fixed r ≥ 3. We analyze...

On the Minimum Label Spanning Tree Problem

Variable neighborhood search for the cost constrained minimum label spanning tree and label constrained minimum spanning tree problems

Given an undirected graph whose edges are labeled or colored, edge weights indicating the cost of an edge, and a positive budget B, the goal of the cost constrained minimum label spanning tree (CCMLST) problem is to find a spanning tree that uses the minimum number of labels while ensuring its cost does not exceed B. The label constrained minimum spanning tree (LCMST) problem is closely related...

Variable Neighborhood Search for the Bounded Diameter Minimum Spanning Tree Problem

The bounded diameter minimum spanning tree problem is an NP-hard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were designed in a way enabling an efficient incremental evaluation and search for the best neighboring s...

Probabilistic Analysis of the Degree Bounded Minimum Spanning Tree Problem

In the b-degree constrained Euclidean minimum spanning tree problem (bMST) we are given n points in [0; 1] and a degree constraint b 2. The aim is to nd a minimum weight spanning tree in which each vertex has degree at most b. In this paper we analyze the probabilistic version of the problem and prove in a rmative the conjecture of Yukich stated in 1998 on the asymptotics of the problem for uni...