14:00
We give a strongly polynomial algorithm for minimum cost generalized flow, and as a consequence, for all linear programs with at most two nonzero entries per row, or at most two nonzero entries per column. While strongly polynomial algorithms for the primal and dual feasibility problems have been known for a long time, various combinatorial approaches used for those problems did not seem to carry over to the minimum-cost variant.
Our approach is to show that the ‘subspace layered least squares’ interior point method, an earlier joint work with Allamigeon, Dadush, Loho and Natura requires only a strongly polynomial number of iterations for minimum cost generalized flow. We achieve this by bounding the straight line complexity, introduced in the same paper. The talk will give an overview of the interior point method as well as the combinatorial straight-line complexity analysis for the particular setting. This is joint work with Daniel Dadush, Zhuan Khye Koh, Bento Natura, and Neil Olver.