Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Batched Set Cover Problem   We introduce the batched set cover problem, which is a generalization of the
online set cover problem. In this problem, the elements of the ground set that
need to be covered arrive in batches. Our main technical contribution is a
tight $\Omega(H_{m - 2^z + 1})$ lower bound on the competitive ratio of any
fractional batched algorithm given an adversary that is required to produce
batches of VC-dimension at least $z$, for some $z \in \mathbb{N}^0$. This
restriction on the adversary is motivated by the fact that, in some real world
applications, decisions are made after collecting batches of data of
non-trivial VC-dimension. In particular, ridesharing systems rely on the batch
assignment of trip requests to vehicles, and some related problems such as that
of optimal congregation points for passenger pickups and dropoffs can be
modeled as a batched set cover problem with VC-dimension greater than or equal
to two. Furthermore, we note that while any online algorithm may be used to
solve the batched set cover problem by artificially sequencing the elements in
a batch, this procedure may neglect the rich information encoded in the complex
interactions between the elements of a batch and the sets that contain them.
Therefore, we propose a minor modification to an online algorithm found in [8]
to obtain an algorithm that attempts to exploit such information.
Unfortunately, we are unable to improve its analysis in a way that reflects
this intuition. However, we present computational experiments that provide
empirical evidence of a constant factor improvement in the competitive ratio.
To the best of our knowledge, we are the first to use the VC-dimension in the
context of online (batched) covering problems.

2
The categories of this paper are: math
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio