In the Minimum Installation Path problem, we are given a graph G with edge weights $w(\cdot )$ and two vertices $s,t$ of G. We want to assign a non-negative power $p:V\to {\mathbb{R}}_{\ge 0}$ to the vertices of G, so that the activated edges $\{uv\in E(G)|p(u)+p(v)\ge w(uv)\}$ contain some s-t-path, and minimize the sum of assigned powers. In the Minimum Barrier Shrinkage problem, we are given, in the plane, a family of disks and two points x and y. The task is to shrink the disks, each one possibly by a different amount, so that we can draw an x-y curve that is disjoint from the interior of the shrunken disks, and the sum of the decreases in the radii is minimized.

We show that the Minimum Installation Path and the Minimum Barrier Shrinkage problems (or, more precisely, the natural decision problems associated with them) are weakly NP-hard.

在最小安装路径问题中，我们得到了带有边权重的图形G$w（\cdot ）$ 和两个顶点 $s，Ť$的ģ。我们想分配一个非负的力量$p：V\to {\mathbb{[R}}_{\ge 0}$到G的顶点，以便激活的边$\{üv\in Ë（G）|p（ü）+p（v）\ge w（üv）\}$包含一些s - t-路径，并最小化分配的功率之和。在最小壁垒收缩问题中，在平面上给出了一组磁盘以及两个点x和y。任务是收缩磁盘，每个磁盘可能收缩不同的量，以便我们可以绘制与收缩的磁盘内部不相交的x - y曲线，并使半径减小的总和最小化。

我们显示最小安装路径和最小壁垒收缩问题（或更准确地说，与它们相关的自然决策问题）对NP的要求较弱。