Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Bounds for Online Weighted Tree Augmentation   The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in
network design. In this paper, we consider this problem in the online setting.
We are given an $n$-vertex spanning tree $T$ and an additional set $L$ of edges
(called links) with costs. Then, terminal pairs arrive one-by-one and our task
is to maintain a low-cost subset of links $F$ such that every terminal pair
that has arrived so far is $2$-edge-connected in $T \cup F$. This online
problem was first studied by Gupta, Krishnaswamy and Ravi (SICOMP 2012) who
used it as a subroutine for the online survivable network design problem. They
gave a deterministic $O(\log^2 n)$-competitive algorithm and showed an
$\Omega(\log n)$ lower bound on the competitive ratio of randomized algorithms.
The case when $T$ is a path is also interesting: it is exactly the online
interval set cover problem, which also captures as a special case the parking
permit problem studied by Meyerson (FOCS 2005). The contribution of this paper
is to give tight results for online weighted tree and path augmentation
problems. The main result of this work is a deterministic $O(\log
n)$-competitive algorithm for online WTAP, which is tight up to constant
factors.

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat