AEON

BMEP

Combinatorial Lower Bounds

Representation of UBTs

Topological Symmetries

The Taxa-Assignment Subproblem

Polyhedral Combinatorics

Facets &Strengthening Valid Inequalities

Lower Bounds

Symmetry Breaking Techniques

Approximating algorithms

Enumeration

Parallel Implicit CPU&GPU based enumeration algorithms

Parallel Brute Force

CPU and GPU-based for the Vertices of the convex hull

Non-isomorphic

Parallel Branch&Cut Algorithms

Parallel B&Cut Algorithms based on Non-Isomorphic Enumeration

Orderings over UBTs

Imbalanced Ordering

Rotation Ordering

Rotation Lattice

Connections with Majorization Lattices

The Optimal Majorization Problem

Reduction Power in P

Study of the Greed Modeling Power

Isomorphism between Lattices

Imbalanced Lattice

Monotonicy and Concavity Analysis of the BMEP objective function over the majorization lattice

NP-Hardness

Conditions for the persistence of the isomorphism

Insights on the NP-hardness of the BMEP

Breaking of Shur-Concavity

Characterization of the versions of the BMEP solvable in polynomial-time via greedy algorithms

Characterization of the problems solvable in polynomial-time via greedy algorithms

Connections with the Huffman Coding Problem

The BMEP as Cross-Entropy Minimization

The BMEP as a compression scheme

Lower-Bounds on the value of the optimal solution inspired by Information theory

Impact on the statistica consistency of the BMEP

The BMEP as an encryption scheme

Hierarchical relationships between the BMEP &MEP

The MEP as master Problem in Distance Methods

Impact on the statistica consistency of distance methods

The MPP as special case of the MEP

A new justification of the general inconsistency of the MPP

Polyhedral combinatorics of the MEP

Preliminary development of parallel Brand&Cut Algorithms for the MEP

Polyhedral combinatorics of the MPP

Preliminary development of parallel Branch&Cut Algorithms for the MPP

feedbacks

Analysis of the loss of concavity in specific models based on Maximum Likelihood

development of possible ways around (i.e., bounds on the likelihood score of a phylogeny) OR proof of the inconsistency of these models

Development of new approximating schemes

Computational analysis and comparison with the current state-of-the-art for the BMEP

Possible detention of this meaning to maximum likelihood estimation models? If yes, How? Why? Which consequences?

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