Greedy strikes back: improved facility location algorithms
Journal of Algorithms
IEEE Computer Graphics and Applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Facility location and the analysis of algorithms through factor-revealing programs
Facility location and the analysis of algorithms through factor-revealing programs
Improved approximation for universal facility location
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
k-means++: the advantages of careful seeding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Lower-bounded facility location
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Improved approximation algorithms for the minimum latency problem via prize-collecting strolls
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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In this paper, we consider the problem of "importance sampling" from a high dynamic range image, motivated by a computer graphics problem called image-based lighting. Image-based lighting is a method to light a scene by using real-world 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 V-shaped facility costs that achieve a minimum at the "ideal" level of demand. We call this the load-balanced facility location problem, and it is a generalization of the uncapacitated facility location problem with uniform facility costs. We develop a primal-dual 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 our algorithm to instances derived from real high dynamic range images.