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On Solving the Minimum Spanning Tree Problem with Conflicting Edge Pairs

Roberto Montemanni, Derek H. Smith

TL;DR

A mixed-integer linear program not previously applied to this problem is presented, and it is shown that the approach it is proposed obtains results aligned with those of the much more sophisticated approaches available, notwithstanding it being much simpler to implement.

Abstract

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches, both heuristic and exact, have been proposed to attack the problem. In this paper we consider a mixed integer linear program never approached before in the context of the problem under investigation, and we solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. The results indicate that the approach we propose, in its simplicity, obtains results aligned with those of the much more sophisticated approaches available. During the experimental campaign 6 instances have been closed for the first time, with 9 improved best-known lower bounds and 16 improved best-known upper bounds over the 230 instances considered.

On Solving the Minimum Spanning Tree Problem with Conflicting Edge Pairs

TL;DR

A mixed-integer linear program not previously applied to this problem is presented, and it is shown that the approach it is proposed obtains results aligned with those of the much more sophisticated approaches available, notwithstanding it being much simpler to implement.

Abstract

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches, both heuristic and exact, have been proposed to attack the problem. In this paper we consider a mixed integer linear program never approached before in the context of the problem under investigation, and we solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. The results indicate that the approach we propose, in its simplicity, obtains results aligned with those of the much more sophisticated approaches available. During the experimental campaign 6 instances have been closed for the first time, with 9 improved best-known lower bounds and 16 improved best-known upper bounds over the 230 instances considered.

Paper Structure

This paper contains 7 sections, 1 equation, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Problem Description
  3. A Mixed Integer Linear Programming Model
  4. Computational Experiments
  5. Benchmark Instances
  6. Experimental Results
  7. Conclusions

Figures (1)

  • Figure 1: On the left an example of a small MSTC instance is shown, where the edge capacities are placed by the edges. Edges in black are not affected by conflicts while any two edges sharing the same red, blue or green color are in conflict. On the right, an optimal solution that does not violate any conflict is shown.