6 citations · 8 across the 6 of their papers we have counts for
10 papers
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…
Improving the Cook et al. Proximity Bound Given Integral Valued Constraints
Marcel Celaya, Stefan Kuhlmann, Joseph Paat +1
Consider a linear program of the form , where is an integral matrix. In 1986 Cook, Gerards, Schrijver, and Tardos proved that, given an op…
Constructing lattice-free gradient polyhedra in dimension two
Joseph Paat, Miriam Schlöter, Emily Speakman
Lattice-free gradient polyhedra can be used to certify optimality for mixed-integer convex minimization models. We consider how to construct these polyhedra for unconstrained model…
Improving proximity bounds using sparsity
Jon Lee, Joseph Paat, Ingo Stallknecht +1
We refer to the distance between optimal solutions of integer programs and their linear relaxations as proximity. In 2018, Eisenbrand and Weismantel proved that proximity is indepe…
Sparsity of integer solutions in the average case
Timm Oertel, Joseph Paat, Robert Weismantel
We examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a…