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AEON (BMEP (Representation of UBTs (Enumeration (Parallel Brute Force (Non…
AEON
BMEP
Representation of UBTs
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 B&Cut Algorithms based on Non-Isomorphic Enumeration
Orderings over UBTs
Imbalanced Ordering
Imbalanced Lattice
Rotation Ordering
Rotation Lattice
Connections with Majorization Lattices
The Optimal Majorization Problem
Reduction Power in P
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
Study of the Greed Modeling Power
Isomorphism between Lattices
Conditions for the persistence of the isomorphism
Insights on the NP-hardness of the BMEP
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Monotonicy and Concavity Analysis of the BMEP objective function over the majorization lattice
Breaking of Shur-Concavity
Topological Symmetries
The Taxa-Assignment Subproblem
NP-Hardness
Approximating algorithms
Development of new approximating schemes
Computational analysis and comparison with the current state-of-the-art for the BMEP
Combinatorial Lower Bounds
Polyhedral Combinatorics
Facets &Strengthening Valid Inequalities
Parallel Branch&Cut Algorithms
Lower Bounds
Symmetry Breaking Techniques
Connections with the Huffman Coding Problem
The BMEP as Cross-Entropy Minimization
The BMEP as a compression scheme
The BMEP as an encryption scheme
Lower-Bounds on the value of the optimal solution inspired by Information theory
Impact on the statistica consistency of the BMEP
Impact on the statistica consistency of distance methods
A new justification of the general inconsistency of the MPP
Possible detention of this meaning to maximum likelihood estimation models? If yes, How? Why? Which consequences?
Hierarchical relationships between the BMEP &MEP
The MEP as master Problem in Distance Methods
The MPP as special case of the MEP
Polyhedral combinatorics of the MPP
Preliminary development of parallel Branch&Cut Algorithms for the MPP
Polyhedral combinatorics of the MEP
Preliminary development of parallel Brand&Cut Algorithms for the MEP
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