The {\em line sum optimization problem} asks for a $(0,1)$-matrix minimizing the sum of given functions evaluated at its row and column sums. We show that the {\em uniform} problem, with identical row functions and identical column functions, and the {\em monotone} problem, over matrices with nonincreasing row and column sums, are polynomial time solvable.
翻译:$[0,1]$-matrix 要求将在行和列总和上评价的给定函数的总和最小化为$(0,1,1)$-matrix。 我们显示, {em uniflig} 的问题, 与行函数和列函数相同, 与 {em 单列函数 和 {em 问题, 与不增加行和列总和的矩阵相比, 是多元时间可溶的 。