Given a n points in two dimensional space, a Manhattan Network G is a network that connects all n points with either horizontal or vertical edges, with the property that for any two point in G should be connected by a Manhattan path and distance between this two points is equal to Manhattan Distance. The Minimum Manhattan Network problem is to find a Manhattan network with minimum network length, i.e., summation of all line segment in network should be minimize. In this paper, we proposed a 2-approximation algorithm with time complexity O(|E|lgN) where |E| is the number of edges and N is the number of nodes. Using randomly generated datasets, we compare our result with the optimal one.

翻译：给定二维空间中的n个点，曼哈顿网络G是一种通过水平或垂直边连接所有n个点的网络，且满足G中任意两点之间存在一条曼哈顿路径，该两点间的距离等于曼哈顿距离。最小曼哈顿网络问题旨在寻找具有最小网络长度的曼哈顿网络，即网络中所有线段长度之和需最小化。本文提出了一种时间复杂度为O(|E|lgN)的2-近似算法，其中|E|为边数，N为节点数。通过随机生成的数据集，我们将本算法结果与最优解进行了比较。