# Minimum weight clustered dominating tree problem

Published: 8 August 2022| Version 1 | DOI: 10.17632/fzd5ndbxsy.1
Contributors:

## Description

This data set corresponds to the instances used in the paper "Minimum weight clustered dominating tree problem" submitted to the European Journal of Operational Research. Each file corresponds to an Euclidean instance. Nodes were randomly generated in a 100 x 100 square meters box. Two nodes i and j are connected by an edge {i,j} if their Euclidian distance is at most the value of the coverage radius in meters. The file name is: "den"+"RadiusValue"+"mts"+"Nodes_"+"NumberOfNodes_"+"Sequential"+".txt" The instance files of the Clustered Dominating Tree Problem contain in the first line the number of nodes |V| and of edges |E| of the connected undirected graph G=(V,E). Line 1: |V| |E| The remaining lines, one for each edge {i,j} in E, give the edge extremities i and j and its cost c(i,j). Lines from 2 to |E|+1: i j c(i,j)

## Steps to reproduce

These instances have 100, 110, 120, 130, 140, and 150 nodes (points in the Euclidean plan). For every number of nodes, we generate five instances with a given radius of distance in the plan. We adopt values for the radius in the set {15, 20, 25, 30}. Two nodes at a distance of at most the given radius are connected by an edge whose weight is the Euclidean distance between them. We generate five instances for each combination of |V| and value of radius. The problem is to find a clustered dominating tree topology of minimum cost for these instances with the use of mathematical integer programming models. Further details on the clustered topology, as well as on solution approaches to handle this problem, can be found in the corresponding paper submitted to EJOR.

## Institutions

Universidad de Santiago de Chile, Universidade Federal do Ceara

## Categories

Operations Research, Combinatorial Optimization