 
Summary: Importance Sampling via
LoadBalanced Facility Location
Aaron Archer and Shankar Krishnan
AT&T LabsResearch, 180 Park Avenue, Florham Park, NJ 07932.
{aarcher,krishnas}@research.att.com
Abstract. In this paper, we consider the problem of "importance sampling" from
a high dynamic range image, motivated by a computer graphics problem called
imagebased lighting. Imagebased lighting is a method to light a scene by using
realworld images as part of a 3D environment. Intuitively, the sampling problem
reduces to finding representative points from the image such that they have higher
density in regions of high intensity (or energy) and low density in regions of low
intensity (or energy).
We formulate this task as a facility location problem where the facility costs are
a function of the demand served. In particular, we aim to encourage load balance
amongst the facilities by using Vshaped facility costs that achieve a minimum
at the "ideal" level of demand. We call this the loadbalanced facility location
problem, and it is a generalization of the uncapacitated facility location problem
with uniform facility costs. We develop a primaldual approximation algorithm
for this problem, and analyze its approximation ratio using dual fitting and factor
revealing linear programs. We also give some experimental results from applying
