On Allocating Goods to Maximize Fairness

Given a set A of m agents and a set I of n items, where agent A ∈ A has utility uA,i for item i ∈ I, our goal is to allocate items to agents to maximize fairness. Specifically, the utility of an agent is the sum of the utilities for items it receives, and we seek to maximize the minimum utility of any agent. While this problem has received much attention recently, its approximability has not been well-understood thus far: the best known approximation algorithm achieves an ˜O( √ m)-approximation, and in contrast, the best known hardness of approximation stands at 2. Our main result is an approximation algorithm that achieves an ˜O(n ) approximation for any = Ω(log log n/ log n) in time nO(1/ ) . In particular, we obtain poly-logarithmic approximation in quasi-polynomial time, and for every constant > 0, we obtain ˜O(n )-approximation in polynomial time. An interesting technical aspect of our algorithm is that we use as a building block a linear program whose integrality ...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Deeparnab Chakrabarty, Julia Chuzhoy, Sanjeev Khanna
• Keywords: Approximation Algorithm, Approximation Stands, FOCS 2009, Integrality Gaps, Theoretical Computer Science