Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nearly-Linear Bound for Chasing Nested Convex Bodies   Friedman and Linial introduced the convex body chasing problem to explore the
interplay between geometry and competitive ratio in metrical task systems. In
convex body chasing, at each time step $t \in \mathbb{N}$, the online algorithm
receives a request in the form of a convex body $K_t \subseteq \mathbb{R}^d$
and must output a point $x_t \in K_t$. The goal is to minimize the total
movement between consecutive output points, where the distance is measured in
some given norm.
  This problem is still far from being understood, and recently Bansal et al.
gave an algorithm for the nested version, where each convex body is contained
within the previous one. We propose a different strategy which is $O(d \log
d)$-competitive algorithm for this nested convex body chasing problem,
improving substantially over previous work. Our algorithm works for any norm.
This result is almost tight, given an $\Omega(d)$ lower bound for the
$\ell_{\infty}$.

12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas