Theoretical Computer Science ( IF 1.1 ) Pub Date : 2020-11-06 , DOI: 10.1016/j.tcs.2020.11.002 C.J. Ras , M. Brazil , D.A. Thomas
The geometric 2-connected Steiner network problem asks for a shortest bridgeless network spanning a given set of terminals in the plane such that the total length of all edges of the network, as measured in the metric, is a minimum. Using reduction from the problem of deciding the Hamiltonicity of planar cubic bipartite graphs we show that this problem is NP-hard (and NP-complete when discretised) for any constant or . Our reduction shows that the geometric 2-connected spanning network problem, i.e., the analogous problem without Steiner points, is also NP-hard for or .
中文翻译:
在2-连通Steiner网络问题的计算复杂度ℓ p平面
几何2连通的Steiner网络问题要求一个最短的无桥网络跨越平面中的一组给定端子,以使网络的所有边缘的总长度(如在 指标,是最小值。使用确定平面三次二分图的汉密尔顿性的问题的减少,我们表明对于任何常数,该问题都是NP-困难的(离散时为NP-完全的) 要么 。我们的减少表明,几何2连通生成网络问题,即没有Steiner点的类似问题,对于 要么 。