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

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 and Ant Colony Optimization for the Rooted Delay-Constrained Minimum Spanning Tree Problem

The rooted delay-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem arising for example in the design of centralized broadcasting networks where quality of service constraints are of concern. We present two new approaches to solve this problem heuristically following the concepts of ant colony optimization (ACO) and variable neighborhood search (VNS). The...

On the Minimum Label Spanning Tree Problem

Variable neighborhood search for the degree-constrained minimum spanning tree problem

Given an undirected graph with weights associated with its edges, the degree-constrained minimum spanning tree problem consists in nding a minimum spanning tree of the given graph, subject to constraints on node degrees. We propose a variable neighborhood search heuristic for the degree-constrained minimum spanning tree problem, based on a dynamic neighborhood model and using a variable neighbo...

The delay-constrained minimum spanning tree problem

We formulate the problem of constructing broadcast trees for real-time traffic with delay constraints in networks with asymmetric link loads as a delay-constrained minimum spanning tree (DCMST) problem in directed networks. Then, we prove that this problem is NP-complete, and we propose an efficient heuristic to solve the problem based on Prim’s algorithm for the unconstrained minimum spanning ...