11,109 research outputs found
Balanced Allocation on Graphs: A Random Walk Approach
In this paper we propose algorithms for allocating sequential balls into
bins that are interconnected as a -regular -vertex graph , where
can be any integer.Let be a given positive integer. In each round
, , ball picks a node of uniformly at random and
performs a non-backtracking random walk of length from the chosen node.Then
it allocates itself on one of the visited nodes with minimum load (ties are
broken uniformly at random). Suppose that has a sufficiently large girth
and . Then we establish an upper bound for the maximum number
of balls at any bin after allocating balls by the algorithm, called {\it
maximum load}, in terms of with high probability. We also show that the
upper bound is at most an factor above the lower bound that is
proved for the algorithm. In particular, we show that if we set , for every constant , and
has girth at least , then the maximum load attained by the
algorithm is bounded by with high probability.Finally, we
slightly modify the algorithm to have similar results for balanced allocation
on -regular graph with and sufficiently large girth
Partitioned Sampling of Public Opinions Based on Their Social Dynamics
Public opinion polling is usually done by random sampling from the entire
population, treating individual opinions as independent. In the real world,
individuals' opinions are often correlated, e.g., among friends in a social
network. In this paper, we explore the idea of partitioned sampling, which
partitions individuals with high opinion similarities into groups and then
samples every group separately to obtain an accurate estimate of the population
opinion. We rigorously formulate the above idea as an optimization problem. We
then show that the simple partitions which contain only one sample in each
group are always better, and reduce finding the optimal simple partition to a
well-studied Min-r-Partition problem. We adapt an approximation algorithm and a
heuristic algorithm to solve the optimization problem. Moreover, to obtain
opinion similarity efficiently, we adapt a well-known opinion evolution model
to characterize social interactions, and provide an exact computation of
opinion similarities based on the model. We use both synthetic and real-world
datasets to demonstrate that the partitioned sampling method results in
significant improvement in sampling quality and it is robust when some opinion
similarities are inaccurate or even missing
A Statistical Mechanical Load Balancer for the Web
The maximum entropy principle from statistical mechanics states that a closed
system attains an equilibrium distribution that maximizes its entropy. We first
show that for graphs with fixed number of edges one can define a stochastic
edge dynamic that can serve as an effective thermalization scheme, and hence,
the underlying graphs are expected to attain their maximum-entropy states,
which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a
rate-equation based analysis of node degree distribution does indeed confirm
the maximum-entropy principle, and (ii) the edge dynamic can be effectively
implemented using short random walks on the underlying graphs, leading to a
local algorithm for the generation of ER random graphs. The resulting
statistical mechanical system can be adapted to provide a distributed and local
(i.e., without any centralized monitoring) mechanism for load balancing, which
can have a significant impact in increasing the efficiency and utilization of
both the Internet (e.g., efficient web mirroring), and large-scale computing
infrastructure (e.g., cluster and grid computing).Comment: 11 Pages, 5 Postscript figures; added references, expanded on
protocol discussio
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
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