Reverse Chvátal--Gomory Rank
نویسندگان
چکیده
منابع مشابه
Totally tight Chvátal-Gomory cuts
Let P := {x∈Rn: Ax6 b} be a polyhedron and PI its integral hull. A Chv atal–Gomory (CG) cut is a valid inequality for PI of the form ( A)x6 b , with ∈R+; TA∈ Z and b ∈ Z . We give a polynomial-time algorithm which, given some x∗ ∈P, detects whether a totally tight CG cut exists, i.e., whether there is a CG cut such that ( TA)x∗= b. Such a CG cut is violated by as much as possible under the assu...
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Chvátal-Gomory and Gomory fractional cuts are well-known cutting planes for pure integer programming problems. Various methods for strengthening them are known, for example based on subadditive functions or disjunctive techniques. We present a new and surprisingly simple strengthening procedure, discuss its properties, and present some computational results.
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In this work, we study the strength of the Chvátal-Gomory cut generating procedure for several hard optimization problems. For hypergraph matching on k-uniform hypergraphs, we show that using Chvátal-Gomory cuts of low rank can reduce the integrality gap significantly even though Sherali-Adams relaxation has a large gap even after linear number of rounds. On the other hand, we show that for oth...
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Given the integer polyhedron PI convfx Z n Ax bg where A Z n and b Zm a Chv atal Gomory CG cut is a valid inequality for PI of the type Ax b bc for some R such that A Z In this paper we study f g CG cuts arising for f g m We show that the associated separa tion problem f g SEP is equivalent to nding a minimum weight member of a binary clutter This implies that f g SEP is NP hard in the general ...
متن کاملCharacterizing Polytopes Contained in the $0/1$-Cube with Bounded Chvátal-Gomory Rank
Let S ⊆ {0, 1} and R be any polytope contained in [0, 1] with R ∩ {0, 1} = S. We prove that R has bounded Chvátal-Gomory rank (CG-rank) provided that S has bounded pitch and bounded gap, where the pitch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the facet coefficients of conv(S). Let H [...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140959882