Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Algorithms for Semi-Matching Problems   We consider the problem of finding \textit{semi-matching} in bipartite graphs
which is also extensively studied under various names in the scheduling
literature. We give faster algorithms for both weighted and unweighted case.
  For the weighted case, we give an $O(nm\log n)$-time algorithm, where $n$ is
the number of vertices and $m$ is the number of edges, by exploiting the
geometric structure of the problem. This improves the classical $O(n^3)$
algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi
[Communications of the ACM 1974].
  For the unweighted case, the bound could be improved even further. We give a
simple divide-and-conquer algorithm which runs in $O(\sqrt{n}m\log n)$ time,
improving two previous $O(nm)$-time algorithms by Abraham [MSc thesis,
University of Glasgow 2003] and Harvey, Ladner, Lov\'asz and Tamir [WADS 2003
and Journal of Algorithms 2006]. We also extend this algorithm to solve the
\textit{Balance Edge Cover} problem in $O(\sqrt{n}m\log n)$ time, improving the
previous $O(nm)$-time algorithm by Harada, Ono, Sadakane and Yamashita [ISAAC
2008].

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci