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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