A New Algorithm for the Cake-Cutting Problem of Unequal Shares for Rational Ratios: The Divisor Reduction Method

The cake-cutting problem is a long-researched question of resource allocation. The problem asks the following: How can a group of players fairly divide a continuous resource (the cake) in an efficient manner if each player has a personal valuation of portions of the resource? The definitions of “fair” and “efficient” can easily complicate the problem. A concept of fairness must be defined at a given problem’s outset. Efficiency often refers to using the least amount of divisions (cuts of the cake) possible while still maintaining fairness. The sub-problem of unequal shares asks how the participants can best divide the cake unequally, according to some predetermined ratio. In the case that this ratio is rational, the accepted method for division by unequal shares is the Cut Near-Halves algorithm [1]. Number theory is applied to this problem in a new way, with the express purpose of besting the efficiency of the Cut-Near Halves algorithm. The result is a novel method for division that is both more efficient and optimal more often than Cut Near-Halves. The new algorithm is described and its effectiveness is empirically analyzed.