Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Speeding Up Sparsification using Inner Product Search Data Structures   We present a general framework that utilizes different efficient data
structures to improve various sparsification problems involving an iterative
process. We also provide insights and characterization for different iterative
process, and answer that when should we use which data structures in what type
of problem. We obtain improved running time for the following problems.
  * For constructing linear-sized spectral sparsifier (Batson, Spielman and
Srivastava, 2012), all the existing deterministic algorithms require
$\Omega(d^4)$ time. In this work, we provide the first deterministic algorithm
that breaks that barrier which runs in $O(d^{\omega+1})$ time, where $\omega$
is the exponent of matrix multiplication.
  * For one-sided Kadison-Singer-typed discrepancy problem, we give fast
algorithms for both small and large number of iterations.
  * For experimental design problem, we speed up a key swapping process.
  In the heart of our work is the design of a variety of different inner
product search data structures that have efficient initialization, query and
update time, compatible to dimensionality reduction and robust against adaptive
adversary.

6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph