Complexity of the Multiobjective Spanner Problem
Abstract
In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach allows us to find solutions that offer a viable compromise between cost and utility. Thus, the MSp can be a powerful modeling tool when it comes to the planning of, e.g., infrastructure. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P != NP, neither the non-dominated set nor the set of extreme points can be computed in output-polynomial time, for instances with unit costs and arbitrary graphs. Furthermore, we consider the directed versions of the cases above.
Cite
@article{arxiv.2206.08805,
title = {Complexity of the Multiobjective Spanner Problem},
author = {Fritz Bökler and Henning Jasper},
journal= {arXiv preprint arXiv:2206.08805},
year = {2022}
}