Moving Knife Algorithms A Comparison between Discrete and Exact Solutions

Fair division algorithms, especially the ones that require continuous observation, tend to assume synchronicity in decision making and knife movements in theory. However, in practice, it is not always possible to give an exact solution to a fair division algorithm without making some assumptions or error bounds. As such, we would like implement both an exact and discrete solution to given algorithms and compare how good of an approximation the discrete solution is. In this experiment, we will be implementing this concept to two such algorithms, both Moving Knife algorithms. The first of the two is the classic Moving Knife algorithm, also known as the DubinsSpanier moving knife. The second of the two algorithms is a custom variation to this moving knife algorithm, which we have coined the “Sistla-Fang” Moving Knife algorithm. In both cases, we will compare the discrete and exact solutions and determine how good an approximation the discrete version is. Further, we will compare the two algorithms mentioned and attempt to show that the “SistlaFang” Moving Knife is a more viable option when considering envy-freeness.