Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two vertices that are close to each other are not allowed to be matched simultaneously. We show that the problem is hard to approximate even for paths, and provide constant-factor approximation algorithms for both paths and grids.

翻译：最大两边匹配是一个基本的算法问题, 可以在多元时间解决 。 我们考虑一个自然的变量, 其中存在一个分隔限制 : 一方的脊椎位于一条路径或一个网格上, 不允许同时匹配两个彼此相近的脊椎 。 我们显示, 这个问题甚至很难接近路径, 并且为路径和网格提供恒定要素近似算法 。</s>