How to eat a graph
Markus Chimani, Thomas C. van Dijk, Jan‐Henrik Haunert · 2014
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.