scholarly journals Lower Bounds on the Lattice-Free Rank for Packing and Covering Integer Programs

2019 ◽  
Vol 29 (1) ◽  
pp. 55-76
Author(s):  
Merve Bodur ◽  
Alberto Del Pia ◽  
Santanu S. Dey ◽  
Marco Molinaro
Keyword(s):  
Lower Bounds ◽  
Packing And Covering ◽  
Integer Programs ◽  
Free Rank

scholarly journals The aggregation closure is polyhedral for packing and covering integer programs

2021 ◽  
Author(s):  
Kanstantsin Pashkovich ◽  
Laurent Poirrier ◽  
Haripriya Pulyassary
Keyword(s):  
Packing And Covering ◽  
Integer Programs

scholarly journals Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

2016 ◽  
Vol 157 (1) ◽  
pp. 47-67 ◽  
Author(s):  
Dinakar Gade ◽  
Gabriel Hackebeil ◽  
Sarah M. Ryan ◽  
Jean-Paul Watson ◽  
Roger J.-B. Wets ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Mixed Integer ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm

scholarly journals Lower bounds on the sizes of integer programs without additional variables

2014 ◽  
Vol 154 (1-2) ◽  
pp. 407-425 ◽  
Author(s):  
Volker Kaibel ◽  
Stefan Weltge
Keyword(s):  
Lower Bounds ◽  
Integer Programs

Interval Packing and Covering in the Boolean Lattice

1996 ◽  
Vol 5 (4) ◽  
pp. 373-384 ◽  
Author(s):  
Konrad Engel
Keyword(s):  
Lower Bounds ◽  
Pairwise Disjoint ◽  
Boolean Lattice ◽  
Covering Number ◽  
Matching Number ◽  
Packing And Covering ◽  
Minimum Number ◽  
Fractional Numbers

Let be the hypergraph whose points are the subsets X of [n] := {1,…,n} with l≤ |X| ≤ u, l < u, and whose edges are intervals in the Boolean lattice of the form I = {C ⊆[n] : X⊆C⊆Y} where |X| = l, |Y| = u, X ⊆ Y.We study the matching number i.e. the the maximum number of pairwise disjoint edges, and the covering number i.e. the minimum number of points which cover all edges. We prove that max and that for every ε > 0 the inequalities hold, where for the lower bounds we suppose that n is not too small. The corresponding fractional numbers can be determined exactly. Moreover, we show by construction that

scholarly journals Aggregation-based cutting-planes for packing and covering integer programs

2017 ◽  
Vol 171 (1-2) ◽  
pp. 331-359 ◽  
Author(s):  
Merve Bodur ◽  
Alberto Del Pia ◽  
Santanu S. Dey ◽  
Marco Molinaro ◽  
Sebastian Pokutta
Keyword(s):  
Cutting Planes ◽  
Packing And Covering ◽  
Integer Programs
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