Approximating the Balanced Minimum Evolution Problem
Samuel Fiorini, Gwena\"el Joret
TL;DR
This paper establishes the NP-hardness of the Balanced Minimum Evolution Problem even for metric instances and introduces a 2-approximation algorithm based on minimum spanning trees.
Contribution
It proves a strong inapproximability result and provides the first known MST-based 2-approximation algorithm for the problem.
Findings
NP-hardness for metric instances
Strong inapproximability results
MST-based 2-approximation algorithm
Abstract
We prove a strong inapproximability result for the Balanced Minimum Evolution Problem. Our proof also implies that the problem remains NP-hard even when restricted to metric instances. Furthermore, we give a MST-based 2-approximation algorithm for the problem for such instances.
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