Improved Algorithms for Computing Fisher's Market Clearing Prices

We give the first strongly polynomial time algorithm for computing an equilibrium for the linear utilities case of Fisher's market model. We consider a problem with a set B of buyers and a set C of divisible goods. Each buyer i starts with an initial integral allocation e(i) of money. The integral utility for buyer i of good j is U-ij. We first develop a weakly polynomial time algorithm that runs in O(n(4) log U-max + n(3)e(max)) time, where n = |B| + |G|. We further modify the algorithm so that it runs in O(n(4) log n) time. These algorithms improve upon the previous best running time of O(n(8) log U-max + n(7) log e(max)), due to Devanur et al. [5].