Seminar: Samuel Fiorini (Bruxelles), International speaker

We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles, where k is any constant. Previously, polynomial-time algorithms were only known for k=0 (bipartite graphs) and for k=1. We observe that integer linear programs defined by coefficient matrices with bounded subdeterminants and two nonzeros per column can be also solved in strongly polynomial-time, using a reduction to b-matching. This is joint work with Gwenaël Joret (ULB), Stefan Weltge (TUM) and Yelena Yuditsky (ULB).