In this paper, we study the general restricted inverse assignment problems, in which we can only change the costs of some specific edges of an assignment problem as less as possible, so that a given assignment becomes the optimal one. Under \(l_1\) norm, we formulate this problem as a linear programming. Then we mainly consider two cases. For the case when the specific edges are only belong to the given assignment, we show that this problem can be reduced to some variations of the minimum cost flow problems. For the case when every specific edge does not belong to the given assignment, we show that this problem can be solved by a minimum cost circulation problem. In both cases, we present some combinatorial algorithms which are strongly polynomial. We also study this problem under the \(l_\infty \) norm. We propose a binary search algorithm and prove that the optimal solution can be obtained in polynomial time.

在本文中，我们研究了一般的受限逆分配问题，在该问题中，我们只能尽可能少地更改分配问题的某些特定边的成本，以使给定的分配成为最优分配。根据\（l_1 \）范数，我们将此问题公式化为线性规划。然后我们主要考虑两种情况。对于特定边仅属于给定分配的情况，我们表明可以将此问题简化为最小成本流问题的某些变体。对于每个特定边都不属于给定分配的情况，我们表明可以通过最小成本循环问题解决此问题。在这两种情况下，我们都提出了一些强多项式的组合算法。我们还将在\（l_ \ infty \）规范。我们提出了一种二元搜索算法，并证明可以在多项式时间内获得最优解。