63,353 research outputs found
Ant-Inspired Density Estimation via Random Walks
Many ant species employ distributed population density estimation in
applications ranging from quorum sensing [Pra05], to task allocation [Gor99],
to appraisal of enemy colony strength [Ada90]. It has been shown that ants
estimate density by tracking encounter rates -- the higher the population
density, the more often the ants bump into each other [Pra05,GPT93].
We study distributed density estimation from a theoretical perspective. We
prove that a group of anonymous agents randomly walking on a grid are able to
estimate their density within a small multiplicative error in few steps by
measuring their rates of encounter with other agents. Despite dependencies
inherent in the fact that nearby agents may collide repeatedly (and, worse,
cannot recognize when this happens), our bound nearly matches what would be
required to estimate density by independently sampling grid locations.
From a biological perspective, our work helps shed light on how ants and
other social insects can obtain relatively accurate density estimates via
encounter rates. From a technical perspective, our analysis provides new tools
for understanding complex dependencies in the collision probabilities of
multiple random walks. We bound the strength of these dependencies using
of the underlying graph. Our results extend beyond
the grid to more general graphs and we discuss applications to size estimation
for social networks and density estimation for robot swarms
Measuring degree-degree association in networks
The Pearson correlation coefficient is commonly used for quantifying the
global level of degree-degree association in complex networks. Here, we use a
probabilistic representation of the underlying network structure for assessing
the applicability of different association measures to heavy-tailed degree
distributions. Theoretical arguments together with our numerical study indicate
that Pearson's coefficient often depends on the size of networks with equal
association structure, impeding a systematic comparison of real-world networks.
In contrast, Kendall-Gibbons' is a considerably more robust measure
of the degree-degree association
On Counting Triangles through Edge Sampling in Large Dynamic Graphs
Traditional frameworks for dynamic graphs have relied on processing only the
stream of edges added into or deleted from an evolving graph, but not any
additional related information such as the degrees or neighbor lists of nodes
incident to the edges. In this paper, we propose a new edge sampling framework
for big-graph analytics in dynamic graphs which enhances the traditional model
by enabling the use of additional related information. To demonstrate the
advantages of this framework, we present a new sampling algorithm, called Edge
Sample and Discard (ESD). It generates an unbiased estimate of the total number
of triangles, which can be continuously updated in response to both edge
additions and deletions. We provide a comparative analysis of the performance
of ESD against two current state-of-the-art algorithms in terms of accuracy and
complexity. The results of the experiments performed on real graphs show that,
with the help of the neighborhood information of the sampled edges, the
accuracy achieved by our algorithm is substantially better. We also
characterize the impact of properties of the graph on the performance of our
algorithm by testing on several Barabasi-Albert graphs.Comment: A short version of this article appeared in Proceedings of the 2017
IEEE/ACM International Conference on Advances in Social Networks Analysis and
Mining (ASONAM 2017
Reliable Broadcast to A User Group with Limited Source Transmissions
In order to reduce the number of retransmissions and save power for the
source node, we propose a two-phase coded scheme to achieve reliable broadcast
from the source to a group of users with minimal source transmissions. In the
first phase, the information packets are encoded with batched sparse (BATS)
code, which are then broadcasted by the source node until the file can be
cooperatively decoded by the user group. In the second phase, each user
broadcasts the re-encoded packets to its peers based on their respective
received packets from the first phase, so that the file can be decoded by each
individual user. The performance of the proposed scheme is analyzed and the
rank distribution at the moment of decoding is derived, which is used as input
for designing the optimal BATS code. Simulation results show that the proposed
scheme can reduce the total number of retransmissions compared with the
traditional single-phase broadcast with optimal erasure codes. Furthermore,
since a large number of transmissions are shifted from the source node to the
users, power consumptions at the source node is significantly reduced.Comment: ICC 2015. arXiv admin note: substantial text overlap with
arXiv:1504.0446
Moment-based parameter estimation in binomial random intersection graph models
Binomial random intersection graphs can be used as parsimonious statistical
models of large and sparse networks, with one parameter for the average degree
and another for transitivity, the tendency of neighbours of a node to be
connected. This paper discusses the estimation of these parameters from a
single observed instance of the graph, using moment estimators based on
observed degrees and frequencies of 2-stars and triangles. The observed data
set is assumed to be a subgraph induced by a set of nodes sampled from
the full set of nodes. We prove the consistency of the proposed estimators
by showing that the relative estimation error is small with high probability
for . As a byproduct, our analysis confirms that the
empirical transitivity coefficient of the graph is with high probability close
to the theoretical clustering coefficient of the model.Comment: 15 pages, 6 figure
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