Work

Hardness of Linear Variants of the Balanced Minimum Evolution Problem

Year: 2026

Type: article

Abstract: ABSTRACT A cubic tree is a tree with leaves in which every internal vertex has degree exactly 3. Any such tree can be encoded by a Path‐Length Matrix (PLM), that is, an integer matrix whose th entry gives the number of edges in the unique path between leaves and in . The convex hull of all PLMs associated with cubic trees on leaves defines the PLM‐polytope . In this article, we prove that optimizing a linear function over the PLM‐polytope is strongly ‐hard. This result is motivated by the balanced minimum evolution problem, a highly nonlinear ‐hard network design problem arising in computational biology, whose underlying combinatorial structure is captured by the PLM‐polytope.

Source: Networks

DOI: 10.1002/net.70069

Authors: Daniele Catanzaro, Gwenaël Joret, Brieuc Pierre, Francesco Pisanu

Institutions: UCLouvain, Université Libre de Bruxelles

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Fondation Louvain, Fonds De La Recherche Scientifique - FNRS

Awards: G1037813146, G5835421522, G786477283, G7970228494, G8180812803