Geometric Networks typically are a sparse subgraphs of  a complete graph defined over a set of points embedded in the plane (or space). There are several algorithms which take a complete graph and compute a sparse subgraph satisfying various constraints, e.g.  low diameter, constant degree and fault-tolerant. In our recent work, we have designed algorithms which compute sparse subgraphs of non-complete graphs. Especially, given a k-partite graph, we construct a sparse subgraph consisting of linear number of edges, and show that the shortest path gets stretched by a constant factor.  This result has appeared in SIAM Jl. Computing 38 (5): 1803—1820, 2009. We want to further broaden the scope of this work with the help of a global link student in the following directions (a) Implementation (b) Experimental Study (c) Possibly come up with an algorithm that constructs a planar  subgrap