@inproceedings{c8387f6f125545b7bc42d67f39ac3cfc,

title = "Geometric optimization and sums of algebraic functions",

abstract = "We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of non-negative, constant description-complexity algebraic functions. We first give a FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions, and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum area hulls.",

author = "Antoine Vigneron",

year = "2010",

doi = "10.1137/1.9781611973075.73",

language = "English (US)",

isbn = "9780898717013",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery (ACM)",

pages = "906--917",

booktitle = "Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms",

address = "United States",

note = "21st Annual ACM-SIAM Symposium on Discrete Algorithms ; Conference date: 17-01-2010 Through 19-01-2010",

}