61,329 research outputs found
Adaptive Random Walks on the Class of Web Graph
We study random walk with adaptive move strategies on a class of directed
graphs with variable wiring diagram. The graphs are grown from the evolution
rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A
{\bf 293}, 273 (2001)], and are characterized by a pair of power-law
distributions of out- and in-degree for each value of the parameter ,
which measures the degree of rewiring in the graph. The walker adapts its move
strategy according to locally available information both on out-degree of the
visited node and in-degree of target node. A standard random walk, on the other
hand, uses the out-degree only. We compute the distribution of connected
subgraphs visited by an ensemble of walkers, the average access time and
survival probability of the walks. We discuss these properties of the walk
dynamics relative to the changes in the global graph structure when the control
parameter is varied. For , corresponding to the
world-wide Web, the access time of the walk to a given level of hierarchy on
the graph is much shorter compared to the standard random walk on the same
graph. By reducing the amount of rewiring towards rigidity limit \beta \to
\beta_c \lesss im 0.1, corresponding to the range of naturally occurring
biochemical networks, the survival probability of adaptive and standard random
walk become increasingly similar. The adaptive random walk can be used as an
efficient message-passing algorithm on this class of graphs for large degree of
rewiring.Comment: 8 pages, including 7 figures; to appear in Europ. Phys. Journal
Balancing Global Exploration and Local-connectivity Exploitation with Rapidly-exploring Random disjointed-Trees
Sampling efficiency in a highly constrained environment has long been a major
challenge for sampling-based planners. In this work, we propose
Rapidly-exploring Random disjointed-Trees* (RRdT*), an incremental optimal
multi-query planner. RRdT* uses multiple disjointed-trees to exploit
local-connectivity of spaces via Markov Chain random sampling, which utilises
neighbourhood information derived from previous successful and failed samples.
To balance local exploitation, RRdT* actively explore unseen global spaces when
local-connectivity exploitation is unsuccessful. The active trade-off between
local exploitation and global exploration is formulated as a multi-armed bandit
problem. We argue that the active balancing of global exploration and local
exploitation is the key to improving sample efficient in sampling-based motion
planners. We provide rigorous proofs of completeness and optimal convergence
for this novel approach. Furthermore, we demonstrate experimentally the
effectiveness of RRdT*'s locally exploring trees in granting improved
visibility for planning. Consequently, RRdT* outperforms existing
state-of-the-art incremental planners, especially in highly constrained
environments.Comment: Submitted to IEEE International Conference on Robotics and Automation
(ICRA) 201
Exploring Complex Graphs by Random Walks
We present an algorithm to grow a graph with scale-free structure of {\it
in-} and {\it out-links} and variable wiring diagram in the class of the
world-wide Web. We then explore the graph by intentional random walks using
local next-near-neighbor search algorithm to navigate through the graph. The
topological properties such as betweenness are determined by an ensemble of
independent walkers and efficiency of the search is compared on three different
graph topologies. In addition we simulate interacting random walks which are
created by given rate and navigated in parallel, representing transport with
queueing of information packets on the graph.Comment: Latex, 4 figure
Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
We consider the role of network geometry in two types of diffusion processes:
transport of constant-density information packets with queuing on nodes, and
constant voltage-driven tunneling of electrons. The underlying network is a
homogeneous graph with scale-free distribution of loops, which is constrained
to a planar geometry and fixed node connectivity . We determine properties
of noise, flow and return-times statistics for both processes on this graph and
relate the observed differences to the microscopic process details. Our main
findings are: (i) Through the local interaction between packets queuing at the
same node, long-range correlations build up in traffic streams, which are
practically absent in the case of electron transport; (ii) Noise fluctuations
in the number of packets and in the number of tunnelings recorded at each node
appear to obey the scaling laws in two distinct universality classes; (iii) The
topological inhomogeneity of betweenness plays the key role in the occurrence
of broad distributions of return times and in the dynamic flow. The
maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure
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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