Given a set $\cal D$ of unit disks in the plane and a set $C$ of colors. Every disk in $\cal D$ is colored with one of the colors in $C$. Note that multiple disks may be colored with the same color. Every color $c_i \in C$ is associated with a weight $w_i$. for every path $p$ in the plane, we define the weight of $p$ as the sum of the weights of the colors that at least one of the circles with that color is crossed by $p$.  In addition, two points $s$ and $t$ is given in the plane and the goal is to find a path between $s$ and $t$ with the minimum total weight. What is the best approximation factor we can guarantee?
Finding a path crossing minimum number of distinct colors
computational geometry;np hard;approximation