14,832 research outputs found
Transport in networks with multiple sources and sinks
We investigate the electrical current and flow (number of parallel paths)
between two sets of n sources and n sinks in complex networks. We derive
analytical formulas for the average current and flow as a function of n. We
show that for small n, increasing n improves the total transport in the
network, while for large n bottlenecks begin to form. For the case of flow,
this leads to an optimal n* above which the transport is less efficient. For
current, the typical decrease in the length of the connecting paths for large n
compensates for the effect of the bottlenecks. We also derive an expression for
the average flow as a function of n under the common limitation that transport
takes place between specific pairs of sources and sinks
Dynamic algorithms for multicast with intra-session network coding
The problem of multiple multicast sessions with
intra-session network coding in time-varying networks is considered.
The network-layer capacity region of input rates that can be
stably supported is established. Dynamic algorithms for multicast
routing, network coding, power allocation, session scheduling, and
rate allocation across correlated sources, which achieve stability
for rates within the capacity region, are presented. This work
builds on the back-pressure approach introduced by Tassiulas
et al., extending it to network coding and correlated sources. In
the proposed algorithms, decisions on routing, network coding,
and scheduling between different sessions at a node are made
locally at each node based on virtual queues for different sinks.
For correlated sources, the sinks locally determine and control
transmission rates across the sources. The proposed approach
yields a completely distributed algorithm for wired networks.
In the wireless case, power control among different transmitters
is centralized while routing, network coding, and scheduling
between different sessions at a given node are distributed
Graph Orientation and Flows Over Time
Flows over time are used to model many real-world logistic and routing
problems. The networks underlying such problems -- streets, tracks, etc. -- are
inherently undirected and directions are only imposed on them to reduce the
danger of colliding vehicles and similar problems. Thus the question arises,
what influence the orientation of the network has on the network flow over time
problem that is being solved on the oriented network. In the literature, this
is also referred to as the contraflow or lane reversal problem.
We introduce and analyze the price of orientation: How much flow is lost in
any orientation of the network if the time horizon remains fixed? We prove that
there is always an orientation where we can still send of the
flow and this bound is tight. For the special case of networks with a single
source or sink, this fraction is which is again tight. We present
more results of similar flavor and also show non-approximability results for
finding the best orientation for single and multicommodity maximum flows over
time
Transport of multiple users in complex networks
We study the transport properties of model networks such as scale-free and
Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the
conductance between two arbitrarily chosen nodes where each link has the
same unit resistance. Our theoretical analysis for scale-free networks predicts
a broad range of values of , with a power-law tail distribution , where , and is the decay
exponent for the scale-free network degree distribution. We confirm our
predictions by large scale simulations. The power-law tail in leads to large values of , thereby significantly improving the
transport in scale-free networks, compared to Erd\H{o}s-R\'{e}nyi networks
where the tail of the conductivity distribution decays exponentially. We
develop a simple physical picture of the transport to account for the results.
We study another model for transport, the \emph{max-flow} model, where
conductance is defined as the number of link-independent paths between the two
nodes, and find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some differences
emerge. We then extend our study to the case of multiple sources, where the
transport is define between two \emph{groups} of nodes. We find a fundamental
difference between the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an optimal number of
sources, or users, for the max-flow case. A qualitative (and partially
quantitative) explanation is also given
Resiliently evolving supply-demand networks
Peer reviewedPublisher PD
Algorithms for Constructing Overlay Networks For Live Streaming
We present a polynomial time approximation algorithm for constructing an
overlay multicast network for streaming live media events over the Internet.
The class of overlay networks constructed by our algorithm include networks
used by Akamai Technologies to deliver live media events to a global audience
with high fidelity. We construct networks consisting of three stages of nodes.
The nodes in the first stage are the entry points that act as sources for the
live streams. Each source forwards each of its streams to one or more nodes in
the second stage that are called reflectors. A reflector can split an incoming
stream into multiple identical outgoing streams, which are then sent on to
nodes in the third and final stage that act as sinks and are located in edge
networks near end-users. As the packets in a stream travel from one stage to
the next, some of them may be lost. A sink combines the packets from multiple
instances of the same stream (by reordering packets and discarding duplicates)
to form a single instance of the stream with minimal loss. Our primary
contribution is an algorithm that constructs an overlay network that provably
satisfies capacity and reliability constraints to within a constant factor of
optimal, and minimizes cost to within a logarithmic factor of optimal. Further
in the common case where only the transmission costs are minimized, we show
that our algorithm produces a solution that has cost within a factor of 2 of
optimal. We also implement our algorithm and evaluate it on realistic traces
derived from Akamai's live streaming network. Our empirical results show that
our algorithm can be used to efficiently construct large-scale overlay networks
in practice with near-optimal cost
Evolutionary Approaches to Minimizing Network Coding Resources
We wish to minimize the resources used for network coding while achieving the
desired throughput in a multicast scenario. We employ evolutionary approaches,
based on a genetic algorithm, that avoid the computational complexity that
makes the problem NP-hard. Our experiments show great improvements over the
sub-optimal solutions of prior methods. Our new algorithms improve over our
previously proposed algorithm in three ways. First, whereas the previous
algorithm can be applied only to acyclic networks, our new method works also
with networks with cycles. Second, we enrich the set of components used in the
genetic algorithm, which improves the performance. Third, we develop a novel
distributed framework. Combining distributed random network coding with our
distributed optimization yields a network coding protocol where the resources
used for coding are optimized in the setup phase by running our evolutionary
algorithm at each node of the network. We demonstrate the effectiveness of our
approach by carrying out simulations on a number of different sets of network
topologies.Comment: 9 pages, 6 figures, accepted to the 26th Annual IEEE Conference on
Computer Communications (INFOCOM 2007
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