/Multi-Level-Graph-Spanners

A graph spanner is an open NP-complete problem, dealing with approximating shortest-path optimizations in a very dense graph. A spanner is a (usually sparse) graph whose shortest path distances approximate the original graph's distances (in the dense graph). The goal is to find a weighted graph over a set of points as its vertices for which there is a t-path between any pair of vertices for a fixed parameter t. A t-path is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner.

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