Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expected time complexity of the auction algorithm and the push relabel
  algorithm for maximal bipartite matching on random graphs   In this paper we analyze the expected time complexity of the auction
algorithm for the matching problem on random bipartite graphs. We prove that
the expected time complexity of the auction algorithm for bipartite matching is
$O\left(\frac{N\log^2(N)}{\log\left(Np\right)}\right)$ on sequential machines.
This is equivalent to other augmenting path algorithms such as the HK
algorithm. Furthermore, we show that the algorithm can be implemented on
parallel machines with $O(\log(N))$ processors and shared memory with an
expected time complexity of $O(N\log(N))$.

33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
16
The categories of this paper are: stat