How to eat a graph: computing selection sequences for the continuous generalization of road networks

In a connected weighted graph, consider deleting the edges one at a time, in some order, such that after every deletion the remaining edges are still connected. We study the problem of finding such a deletion sequence that maximizes the sum of the weights of the edges in all the distinct graphs generated: the weight of an edge is counted in every graph that it is in. This effectively asks for the high-weight edges to remain in the graph as long as possible, subject to connectivity. We apply this to road network generalization in order to generate a sequence of successively more generalized maps of a road network so that these maps go well together, instead of considering each level of generalization independently. In particular, we look at the problem of making a road segment selection that is consistent across zoom levels. We show that the problem is NP-hard and give an integer linear program (ILP) that solves it optimally. Solving this ILP is only feasible for small instances. Next we develop constant-factor approximation algorithms and heuristics. We experimentally demonstrate that these heuristics perform well on real-world instances.