Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalable Percolation Search in Power Law Networks   We introduce a scalable searching algorithm for finding nodes and contents in
random networks with Power-Law (PL) and heavy-tailed degree distributions. The
network is searched using a probabilistic broadcast algorithm, where a query
message is relayed on each edge with probability just above the bond
percolation threshold of the network. We show that if each node caches its
directory via a short random walk, then the total number of {\em accessible
contents exhibits a first-order phase transition}, ensuring very high hit rates
just above the percolation threshold. In any random PL network of size, $N$,
and exponent, $2 \leq \tau < 3$, the total traffic per query scales
sub-linearly, while the search time scales as $O(\log N)$. In a PL network with
exponent, $\tau \approx 2$, {\em any content or node} can be located in the
network with {\em probability approaching one} in time $O(\log N)$, while
generating traffic that scales as $O(\log^2 N)$, if the maximum degree,
$k_{max}$, is unconstrained, and as $O(N^{{1/2}+\epsilon})$ (for any
$\epsilon>0$) if $ k_{max}=O(\sqrt{N})$. Extensive large-scale simulations show
these scaling laws to be precise. We discuss how this percolation search
algorithm can be directly adapted to solve the well-known scaling problem in
unstructured Peer-to-Peer (P2P) networks. Simulations of the protocol on sample
large-scale subnetworks of existing P2P services show that overall traffic can
be reduced by almost two-orders of magnitude, without any significant loss in
search performance.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th