30 research outputs found
EZ-AG: Structure-free data aggregation in MANETs using push-assisted self-repelling random walks
This paper describes EZ-AG, a structure-free protocol for duplicate
insensitive data aggregation in MANETs. The key idea in EZ-AG is to introduce a
token that performs a self-repelling random walk in the network and aggregates
information from nodes when they are visited for the first time. A
self-repelling random walk of a token on a graph is one in which at each step,
the token moves to a neighbor that has been visited least often. While
self-repelling random walks visit all nodes in the network much faster than
plain random walks, they tend to slow down when most of the nodes are already
visited. In this paper, we show that a single step push phase at each node can
significantly speed up the aggregation and eliminate this slow down. By doing
so, EZ-AG achieves aggregation in only O(N) time and messages. In terms of
overhead, EZ-AG outperforms existing structure-free data aggregation by a
factor of at least log(N) and achieves the lower bound for aggregation message
overhead. We demonstrate the scalability and robustness of EZ-AG using ns-3
simulations in networks ranging from 100 to 4000 nodes under different mobility
models and node speeds. We also describe a hierarchical extension for EZ-AG
that can produce multi-resolution aggregates at each node using only O(NlogN)
messages, which is a poly-logarithmic factor improvement over existing
techniques
The acquaintance time of (percolated) random geometric graphs
In this paper, we study the acquaintance time \AC(G) defined for a
connected graph . We focus on \G(n,r,p), a random subgraph of a random
geometric graph in which vertices are chosen uniformly at random and
independently from , and two vertices are adjacent with probability
if the Euclidean distance between them is at most . We present
asymptotic results for the acquaintance time of \G(n,r,p) for a wide range of
and . In particular, we show that with high probability
\AC(G) = \Theta(r^{-2}) for G \in \G(n,r,1), the "ordinary" random
geometric graph, provided that (that is, above
the connectivity threshold). For the percolated random geometric graph G \in
\G(n,r,p), we show that with high probability \AC(G) = \Theta(r^{-2} p^{-1}
\ln n), provided that p n r^2 \geq n^{1/2+\eps} and p < 1-\eps for some
\eps>0
On the Mixing Time of Geographical Threshold Graphs
We study the mixing time of random graphs in the -dimensional toric unit
cube generated by the geographical threshold graph (GTG) model, a
generalization of random geometric graphs (RGG). In a GTG, nodes are
distributed in a Euclidean space, and edges are assigned according to a
threshold function involving the distance between nodes as well as randomly
chosen node weights, drawn from some distribution. The connectivity threshold
for GTGs is comparable to that of RGGs, essentially corresponding to a
connectivity radius of . However, the degree distributions
at this threshold are quite different: in an RGG the degrees are essentially
uniform, while RGGs have heterogeneous degrees that depend upon the weight
distribution. Herein, we study the mixing times of random walks on
-dimensional GTGs near the connectivity threshold for . If the
weight distribution function decays with for an arbitrarily small constant then the mixing time
of GTG is \mixbound. This matches the known mixing bounds for the
-dimensional RGG