Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online Matroid Intersection: Beating Half for Random Arrival   For two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ defined on the same
ground set $E$, the online matroid intersection problem is to design an
algorithm that constructs a large common independent set in an online fashion.
The algorithm is presented with the ground set elements one-by-one in a
uniformly random order. At each step, the algorithm must irrevocably decide
whether to pick the element, while always maintaining a common independent set.
While the natural greedy algorithm---pick an element whenever possible---is
half competitive, nothing better was previously known; even for the special
case of online bipartite matching in the edge arrival model. We present the
first randomized online algorithm that has a $\frac12 + \delta$ competitive
ratio in expectation, where $\delta >0$ is a constant. The expectation is over
the random order and the coin tosses of the algorithm. As a corollary, we also
obtain the first linear time algorithm that beats half competitiveness for
offline matroid intersection.

35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph