14 citations · 30 across the 20 of their papers we have counts for
5 papers · 1 filter
On the column number and forbidden submatrices for -modular matrices
Joseph Paat, Ingo Stallknecht, Zach Walsh +1
An integer matrix is -modular if the determinant of each submatrix of has absolute value at mo…
Proximity and flatness bounds for linear integer optimization
Marcel Celaya, Stefan Kuhlmann, Joseph Paat +1
We develop a technique that can be applied to provide improved upper bounds for two important questions in linear integer optimization. - Proximity bounds: Given an optimal vertex…
A characterization of maximal homogeneous-quadratic-free sets
Gonzalo Muñoz, Joseph Paat, Felipe Serrano
The intersection cut framework was introduced by Balas in 1971 as a method for generating cutting planes in integer optimization. In this framework, one uses a full-dimensional con…
Compressing Branch-and-Bound Trees
Gonzalo Muñoz, Joseph Paat, Álinson S. Xavier
A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certif…
A Colorful Steinitz Lemma with Applications to Block Integer Programs
Timm Oertel, Joseph Paat, Robert Weismantel
The Steinitz constant in dimension is the smallest value such that for any norm on and for any finite zero-sum sequence in the unit ball, the sequence…