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  • Authors: Ailon, Nir (2006)

  • This work is comprised of three separate parts: (1) Lower bounds for linear degeneracy testing (based on joint work with Bernard Chazelle [5]); (2) Aggregating inconsistent information (based on joint work with Moses Charikar and Alantha Newman [3]); and (3) The fast Johnson-Lindenstrauss transform and approximate nearest neighbor searching (based on joint work with Bernard Chazelle [6]). The first part discusses a fundamental computational geometric problem called rSUM: given n real numbers, do any r of them sum up to 0? It is the simplest case of a more general family of problems called degeneracy testing. This seemingly naive problem is in the core of the di cult y in designing algorithms for more interesting problems in computational geometry. The computational model assumed is...