Fair pie-cutting

The fair pie-cutting problem is a variation of the fair cake-cutting problem, in which the resource to be divided is circular. As an example, consider a birthday cake shaped as a disk. The cake should be divided among several children such that no child envies another child (as in a standard cake-cutting problem), with the additional constraint that the cuts must be radial, so that each child receives a circular sector. A possible application of the pie model might be for dividing an island’s shoreline into connected lots.

Fair pie-cutting

The fair pie-cutting problem is a variation of the fair cake-cutting problem, in which the resource to be divided is circular. As an example, consider a birthday cake shaped as a disk. The cake should be divided among several children such that no child envies another child (as in a standard cake-cutting problem), with the additional constraint that the cuts must be radial, so that each child receives a circular sector. A possible application of the pie model might be for dividing an island’s shoreline into connected lots.