124 citations · 566 across the 52 of their papers we have counts for
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Light on the Infinite Group Relaxation
Amitabh Basu, Robert Hildebrand, Matthias Köppe
This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their gro…
Operations that preserve the covering property of the lifting region
Amitabh Basu, Joe Paat
We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain struc…
Lifting properties of maximal lattice-free polyhedra
Gennadiy Averkov, Amitabh Basu
We study the uniqueness of minimal liftings of cut-generating functions obtained from maximal lattice-free polyhedra. We prove a basic invariance property of unique minimal lifting…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2
Amitabh Basu, Robert Hildebrand, Matthias Köppe
We develop foundational tools for classifying the extreme valid functions for the k-dimensional infinite group problem. In particular, (1) we present the general regular solution t…