منابع مشابه
Polyhedral Combinatorics of UPGMA Cones
Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm. The partition lattice informs the study of UPGMA trees. We...
متن کاملRigidity and polyhedral combinatorics
The following compilation of participant contributions is only intended as a lead-in to the AIM workshop " Rigidity and polyhedral combinatorics. " This material is not for public distribution. Corrections and new material are welcomed and can be sent to [email protected]
متن کاملPolyhedral Combinatorics of Benzenoid Problems
Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the linear programming relaxation always yields integral solutions. We prove this conjecture showing...
متن کاملLinear Programming and Polyhedral Combinatorics
This is a special case of a projection onto a linear space (here, we consider only coordinate projection). By repeatedly projecting, we can eliminate any subset of coordinates. We claim that Pk is also a polyhedron and this can be proved by giving an explicit description of Pk in terms of linear inequalities. For this purpose, one uses Fourier-Motzkin elimination. Let P = {x : Ax ≤ b} and let •...
متن کاملPolyhedral combinatorics: An annotated bibliography
The system Bx b is said to describe P , and each hyperplane fx 2 IR : B i x = big is called a cutting plane. One of the central questions in polyhedral combinatorics is to nd the cutting planes that describe P . This question is the subject of this chapter. We start with a section on books and collections of survey articles that treat polyhedral combinatorics in detail. x2 on integer programmin...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2013
ISSN: 0196-8858
DOI: 10.1016/j.aam.2012.10.002