Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asynchronous Rumor Spreading on Random Graphs   We perform a thorough study of various characteristics of the asynchronous
push-pull protocol for spreading a rumor on Erd\H{o}s-R\'enyi random graphs
$G_{n,p}$, for any $p>c\ln(n)/n$ with $c>1$. In particular, we provide a simple
strategy for analyzing the asynchronous push-pull protocol on arbitrary graph
topologies and apply this strategy to $G_{n,p}$. We prove tight bounds of
logarithmic order for the total time that is needed until the information has
spread to all nodes. Surprisingly, the time required by the asynchronous
push-pull protocol is asymptotically almost unaffected by the average degree of
the graph. Similarly tight bounds for Erd\H{o}s-R\'enyi random graphs have
previously only been obtained for the synchronous push protocol, where it has
been observed that the total running time increases significantly for sparse
random graphs. Finally, we quantify the robustness of the protocol with respect
to transmission and node failures. Our analysis suggests that the asynchronous
protocols are particularly robust with respect to these failures compared to
their synchronous counterparts.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an