@inproceedings{ea0d2ba607a34341a456891b3b077a39,

title = "Integer programs with bounded subdeterminants and two nonzeros per row",

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.",

keywords = "integer programming, odd cycle packing number, stable set, subdeterminants",

author = "Samuel Fiorini and Gwenael Joret and Stefan Weltge and Yelena Yuditsky",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 ; Conference date: 07-02-2022 Through 10-02-2022",

year = "2022",

month = jan,

day = "1",

doi = "10.1109/FOCS52979.2021.00011",

language = "English",

series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "13--24",

booktitle = "Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021",

address = "United States",

}