Tuesday, October 29, 2013

[clqpdkir] Voronoi like districting

Need a function of 1 variable and 1 (additional) parameter. Probably monotonically increasing.

A partition of a plane is defined by a set of centers each with a parameter.  The parameters are not constrained to be equal.  Every point on the plane is assigned to the center which minimizes the value of the function evaluated at the distance to that center.

For example, if the function is identity, we would get a Voronoi partition.  With other functions, one can get enclaves and exclaves.

The intended application is political redistricting.  Determining the distance between points is relatively easy compared to determining which side of a line or curve one lives.  We would still need some optimization criterion, e.g., compactness, to select among centers and parameters which divide the population equally.

1 comment :

Anonymous said...

Is what you're proposing similar to this?
http://rangevoting.org/GerryExamples.html