Sensor Cover Problem
Just observations that do not fit on the comments:

I made a little research, and here are what I found + some of my observations: 
1) You can use exhaustive search to find whether a solution exist. [so it is decidable]
2) In case $\delta$ is not restricted, all you need to check is the sum of all ranges and compare it to the distance between the farthest two points. If greater or equal, then there exist a solution. 
3) In case $\delta$ is restricted, then you are trying to restrict the distance traveled by sensors to at most $n \delta$. In case the sensing ranges are not equal, then this problem is still open [1]. 

I would suggest you look in the same reference for a solution for the case of equal sensing ranges. So I think a greedy solution exist.

[1] On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment. J. Czyzowicz , E. Kranakis , D. Krizanc , I. Lambadaris , L. Narayanan , J. Opatrny , L. Stacho , J. Urrutia, and M. Yazdani.