Allocating Goods to Maximize Fairness

April 25, 2011
Julia Chuzhoy | Toyota Technological Institute

We consider the Max-Min Allocation problem, in which we are given a set of m agents and a set of n items, together with utilities u(A,i) of agent A for item i. Our goal is to allocate items to agents to maximize fairness. Specifically, the utility of an agent is the sum of its utilities for the items it receives, and we seek to maximize the minimum utility of any agent. While this problem has received much attention, its approximability has not been well-understood thus far: the best previously known approximation algorithm achieved a roughly O(√ m)-approximation, and in contrast, the best known hardness of approximation stands at factor 2.

We present an approximation algorithm that achieves a ˜O(n^ε) approximation in time n^O(1/ε), for any ε=Ω(log log n/log n). In particular, we obtain poly-logarithmic approximation in quasi-polynomial time, and for every constant ε 0, we obtain an O(n^ε)-approximation in polynomial time.

Joint work with Deeparnab Chakrabarty and Sanjeev Khanna

Speaker Details

Julia Chuzhoy is an Assistant Professor at the Toyota Technological Institute at Chicago. She has obtained Ph. D. from Technion, Israel, and has spent three years as a postdoc at MIT, University of Pennsylvania and Institute for Advanced study, before coming to TTI-C. Her research area is theoretical computer science, with the focus on approximation algorithms for NP-hard combinatorial optimization problems.