Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimization Algorithms for Faster Computational Geometry   We study two fundamental problems in computational geometry: finding the
maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$
hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points,
both in $d$-dimensional space. We improve the running time of iterative
algorithms on
  MaxIB from $\tilde{O}(m d \alpha^3 / \varepsilon^3)$ to $\tilde{O}(md + m
\sqrt{d} \alpha / \varepsilon)$, a speed-up up to $\tilde{O}(\sqrt{d} \alpha^2
/ \varepsilon^2)$, and
  MinEB from $\tilde{O}(n d / \sqrt{\varepsilon})$ to $\tilde{O}(nd + n
\sqrt{d} / \sqrt{\varepsilon})$, a speed-up up to $\tilde{O}(\sqrt{d})$.
  Our improvements are based on a novel saddle-point optimization framework. We
propose a new algorithm $\mathtt{L1L2SPSolver}$ for solving a class of
regularized saddle-point problems, and apply a randomized Hadamard space
rotation which is a technique borrowed from compressive sensing. Interestingly,
the motivation of using Hadamard rotation solely comes from our optimization
view but not the original geometry problem: indeed, it is not immediately clear
why MaxIB or MinEB, as a geometric problem, should be easier to solve if we
rotate the space by a unitary matrix. We hope that our optimization perspective
sheds lights on solving other geometric problems as well.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess