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Integer programs with bounded subdeterminants and two nonzeros per row

par Fiorini, Samuel ;Joret, Gwenaël ;Weltge, Stefan;Yuditsky, Yelena
Référence Annual Symposium on Foundations of Computer Science, page (13-24), FOCS 2021
Publication Publié, 2022-01-01

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Résumé :

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.