Fairness measures for resource allocation

In many optimization problems, one seeks to allocate a limited set of resources to a set of individuals with demands. Thus, such allocations can naturally be viewed as vectors, with one coordinate representing each individual. Motivated by work in network routing and bandwidth assignment, we consider the problem of producing solutions that simultaneously approximate all feasible allocations in a coordinate-wise sense. This is a very strong type of "global" approximation guarantee, and we explore its consequences in a wide range of discrete optimization problems, including facility location, scheduling, and bandwidth assignment in networks. A fundamental issue - one not encountered in the traditional design of approximation algorithms - is that good approximations in this global sense need not exist for every problem instance; there is no a priori reason why there should be an allocation that simultaneously approximates all others. As a result, the existential questions concerning such good allocations lead to a new perspective on a number of fundamental problems in resource allocation, and on the structure of their feasible solutions.