Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Greedy Online Bipartite Matching on Random Graphs   We study the average performance of online greedy matching algorithms on
$G(n,n,p)$, the random bipartite graph with $n$ vertices on each side and edges
occurring independently with probability $p=p(n)$. In the online model,
vertices on one side of the graph are given up front while vertices on the
other side arrive sequentially; when a vertex arrives its edges are revealed
and it must be immediately matched or dropped. We begin by analyzing the
\textsc{oblivious} algorithm, which tries to match each arriving vertex to a
random neighbor, even if the neighbor has already been matched. The algorithm
is shown to have a performance ratio of at least $1-1/e$ for all monotonic
functions $p(n)$, where the performance ratio is defined asymptotically as the
ratio of the expected matching size given by the algorithm to the expected
maximum matching size. Next we show that the conventional \textsc{greedy}
algorithm, which assigns each vertex to a random unmatched neighbor, has a
performance ratio of at least 0.837 for all monotonic functions $p(n)$. Under
the $G(n,n,p)$ model, the performance of \textsc{greedy} is equivalent to the
performance of the well known \textsc{ranking} algorithm, so our results show
that \textsc{ranking} has a performance ratio of at least 0.837. We finally
consider vertex-weighted bipartite matching. Our proofs are based on simple
differential equations that describe the evolution of the matching process.

24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an