Work

Integer programs with bounded subdeterminants and two nonzeros per row

Year: 2024

Type: article

Abstract: 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.

Source: Journal of the ACM

DOI: 10.1145/3695985

Authors: Samuel Fiorini, Gwenaël Joret, Stefan Weltge, Yelena Yuditsky

Institutions: Université Libre de Bruxelles, Technical University of Munich

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Fonds De La Recherche Scientifique - FNRS

Awards: G2054523510, Erweiterte Formulierungen der nächsten Generation