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7 papers
An Integer Program for Pricing Support Points of Exact Barycenters
Steffen Borgwardt, Stephan Patterson
The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions return…
A Note on the Approximability of Deepest-Descent Circuit Steps
Steffen Borgwardt, Cornelius Brand, Andreas Emil Feldmann +1
Linear programs (LPs) can be solved by polynomially many moves along the circuit direction improving the objective the most, so-called deepest-descent steps (dd-steps). Computing t…
An implementation of steepest-descent augmentation for linear programs
Steffen Borgwardt, Charles Viss
Generalizing the simplex method, circuit augmentation schemes for linear programs follow circuit directions through the interior of the underlying polyhedron. Steepest-descent augm…
Constructing Clustering Transformations
Steffen Borgwardt, Charles Viss
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, diff…
A Polyhedral Model for Enumeration and Optimization over the Set of Circuits
Steffen Borgwardt, Charles Viss
Circuits play a fundamental role in polyhedral theory and linear programming. For instance, circuits are used as step directions in various augmentation schemes for solving linear…
Improved Linear Programs for Discrete Barycenters
Steffen Borgwardt, Stephan Patterson
Discrete barycenters are the optimal solutions to mass transport problems for a set of discrete measures. Such transport problems arise in many applications of operations research…