[oizedxmo] State boundaries by travel distance

Partition a region into N smaller regions minimizing the norm of a function F evaluated on each region.

Norm could be maximum, L-infinity norm, yielding a geometric minimax problem.

F could be the radius of the circumcircle of the region.  The center would be a good place to put the state capital.

Radius of the smallest circle which covers 90% of the area of the region.  Or of the population.

The maximum distance between any two points in the region.

The same measures could be asked of partitioning a graph: the travel time graph formed by the network of roads, using graph centers and graph diameters.  This will capture physical barriers across which travel is slow.

Unlike redistricting, there is no constraint of equal population nor equal area.  The idea is a political region is defined by people moving around (or being able to move around) in it.  If using the road graph, states will probably reflect the location of highways.  Large chunks of the east coast might merge.