3,672 research outputs found
Reverse Chv\'atal-Gomory rank
We introduce the reverse Chv\'atal-Gomory rank r*(P) of an integral
polyhedron P, defined as the supremum of the Chv\'atal-Gomory ranks of all
rational polyhedra whose integer hull is P. A well-known example in dimension
two shows that there exist integral polytopes P with r*(P) equal to infinity.
We provide a geometric characterization of polyhedra with this property in
general dimension, and investigate upper bounds on r*(P) when this value is
finite.Comment: 21 pages, 4 figure
Intermediate integer programming representations using value disjunctions
We introduce a general technique to create an extended formulation of a
mixed-integer program. We classify the integer variables into blocks, each of
which generates a finite set of vector values. The extended formulation is
constructed by creating a new binary variable for each generated value. Initial
experiments show that the extended formulation can have a more compact complete
description than the original formulation.
We prove that, using this reformulation technique, the facet description
decomposes into one ``linking polyhedron'' per block and the ``aggregated
polyhedron''. Each of these polyhedra can be analyzed separately. For the case
of identical coefficients in a block, we provide a complete description of the
linking polyhedron and a polynomial-time separation algorithm. Applied to the
knapsack with a fixed number of distinct coefficients, this theorem provides a
complete description in an extended space with a polynomial number of
variables.Comment: 26 pages, 5 figure
Mirror duality and string-theoretic Hodge numbers
We prove in full generality the mirror duality conjecture for
string-theoretic Hodge numbers of Calabi-Yau complete intersections in
Gorenstein toric Fano varieties. The proof is based on properties of
intersection cohomologyComment: 20 pages, Late
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