Debmalya's Paper

Reading Debmalya's paper. He calls the problem Topology Construction (TC). He shows why fixing an MST as an underlying topology does not work.

The key here is that he assigns obstructions to every edge and hence the heights required to cover that edge vary. This is as against our assumption where we consider obstacles to be uniform and uniformly distributed over all edges to give a much simpler height function (indeed a constant one). It remains to be seen whether in practice this is a reasonable simplifying assumption to be made.

With his height function we can no longer think of the space as Euclidean space anymore. He shows under his setting that selecting a MST as the set of edges to be covered is $\Omega(n)$ worse than optimal. \textbf{However we still need to look at this problem in the Euclidean case. We need to keep the directedness aside and look at this problem too.}

\textbf{Some simplifying assumptions that hold in our case and that he does not consider:
1. Two tall towers can see each other regardless of the distance.}

\textbf{An interesting idea is to start off with a network graph - this could be the graph with edges if between vertices if power transmission is possible (not too far) but how do you fit in interference in this ?}

\textbf{Hehehehe ... interestingly it seems they have defined the problem well for us and left it open for us to work on the geometric version of the problem !!!}