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cs.CG2023
Smooth Distance Approximation
Ahmed Abdelkader, David M. Mount
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, b…
cs.DS2023
Linear-Sized Spectral Sparsifiers and the Kadison-Singer Problem
Phevos Paschalidis, Ashley Zhuang
The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava (MSS) [Ann. Math. 182, 327-350 (2015)], has been informally thought of as a strengthening of Batson, Sp…
cs.CG2023
Approximate Nearest Neighbor Searching with Non-Euclidean and Weighted Distances
Ahmed Abdelkader, Sunil Arya, Guilherme D. da Fonseca +1
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set of points in $\mathbb{R}…