Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Bounds for Rumor Spreading with Vertex Expansion   We establish a bound for the classic PUSH-PULL rumor spreading protocol on
arbitrary graphs, in terms of the vertex expansion of the graph. We show that
O(log^2(n)/\alpha) rounds suffice with high probability to spread a rumor from
a single node to all n nodes, in any graph with vertex expansion at least
\alpha. This bound matches the known lower bound, and settles the question on
the relationship between rumor spreading and vertex expansion asked by
Chierichetti, Lattanzi, and Panconesi (SODA 2010). Further, some of the
arguments used in the proof may be of independent interest, as they give new
insights, for example, on how to choose a small set of nodes in which to plant
the rumor initially, to guarantee fast rumor spreading.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex