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.

翻译：我们给出一个极强的多元时间算法,用于由整数系数矩阵定义的整数线性程序,其子确定值受常数约束,且每行最多包含两个非零条目。我们的方法核心是,在不包含超过千元的顶部分解奇数周期的图形中,对加权稳定定数问题的第一个多元时间算法,其中千元是任何常数。以前,多元时间算法仅以美元=0美元(双向图形)和美元=1美元(k=1美元)为已知值。我们观察到,由带带子确定和每列两个非零的系数矩阵定义的整数线性程序也可以在强烈的多元时间中用减为$b$的匹配法加以解决。