It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal.
Typical optimization objectives include:[1] Fair division of land has been an important issue since ancient times, e.g. in ancient Greece.
[2] There is a geographic region denoted by C ("cake").
A partition of C, denoted by X, is a list of disjoint subregions whose union is C: There is a certain set of additional parameters (such as: obstacles, fixed points or probability density functions), denoted by P. There is a real-valued function denoted by G ("goal") on the set of all partitions.
The map segmentation problem is to find: where the minimization is on the set of all partitions of C. Often, there are geometric shape constraints on the partitions, e.g., it may be required that each part be a convex set or a connected set or at least a measurable set.