7,295 research outputs found
Resilience of Partial k-tree Networks with Edge and Node Failures
23 pagesThe resilience of a network is the expected number of pairs of nodes
that can communicate. Computing the resilience of a network is a #P-complete
problem even for planar networks with fail-safe nodes. We generalize
an O(n)^2 time algorithm to compute the resilience of n-node k-tree
networks with fail-safe nodes to obtain an O(n) time algorithm that computes
the resilience of n-node partial k-tree networks with edge and node
failures (given a fixed k and an embedding of the partial k-tree in a k-tree)
Reliability of Partial k-tree Networks
133 pagesRecent developments in graph theory have shown the importance of
the class of partial k- trees. This large class of graphs admits several
algorithm design methodologies that render efficient solutions for a large
number of problems inherently difficult for general graphs. In this thesis
we develop such algorithms to solve a variety of reliability problems on
partial k-tree networks with node and edge failures. We also investigate
the problem of designing uniformly optimal 2-trees with respect to the
2-terminal reliability measure.
We model a. communication network as a graph in which nodes represent
communication sites and edges represent bidirectional communication
lines. Each component (node or edge) has an associated probability of
operation. Components of the network are in either operational or failed
state and their failures are statistically independent. Under this model,
the reliability of a network G is defined as the probability that a given
connectivity condition holds. The l-terminal reliability of G, Rel1 ( G), is
the probability that any two of a given set of I nodes of G can communicate.
Robustness of a network to withstand failures can be expressed
through network resilience, Res( G), which is the expected number of distinct
pairs of nodes that can communicate. Computing these and other
similarly defined measures is #P-hard for general networks.
We use a dynamic programming paradigm to design linear time algorithms that compute Rel1( G), Res( G), and some other reliability and
resilience measures of a partial k-tree network given with an embedding
in a k-tree (for a fixed k).
Reliability problems on directed networks are also inherently difficult.
We present efficient algorithms for directed versions of typical reliability
and resilience problems restricted to partial k-tree networks without node
failures. Then we reduce to those reliability problems allowing both node
and edge failures.
Finally, we study 2-terminal reliability aspects of 2-trees. We characterize
uniformly optimal 2-trees, 2-paths, and 2-caterpillars with respect
to Rel2 and identify local graph operations that improve the 2-terminal
reliability of 2-tree networks
Resilience of Locally Routed Network Flows: More Capacity is Not Always Better
In this paper, we are concerned with the resilience of locally routed network
flows with finite link capacities. In this setting, an external inflow is
injected to the so-called origin nodes. The total inflow arriving at each node
is routed locally such that none of the outgoing links are overloaded unless
the node receives an inflow greater than its total outgoing capacity. A link
irreversibly fails if it is overloaded or if there is no operational link in
its immediate downstream to carry its flow. For such systems, resilience is
defined as the minimum amount of reduction in the link capacities that would
result in the failure of all the outgoing links of an origin node. We show that
such networks do not necessarily become more resilient as additional capacity
is built in the network. Moreover, when the external inflow does not exceed the
network capacity, selective reductions of capacity at certain links can
actually help averting the cascading failures, without requiring any change in
the local routing policies. This is an attractive feature as it is often easier
in practice to reduce the available capacity of some critical links than to add
physical capacity or to alter routing policies, e.g., when such policies are
determined by social behavior, as in the case of road traffic networks. The
results can thus be used for real-time monitoring of distance-to-failure in
such networks and devising a feasible course of actions to avert systemic
failures.Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 201
Local heuristics and the emergence of spanning subgraphs in complex networks
We study the use of local heuristics to determine spanning subgraphs for use
in the dissemination of information in complex networks. We introduce two
different heuristics and analyze their behavior in giving rise to spanning
subgraphs that perform well in terms of allowing every node of the network to
be reached, of requiring relatively few messages and small node bandwidth for
information dissemination, and also of stretching paths with respect to the
underlying network only modestly. We contribute a detailed mathematical
analysis of one of the heuristics and provide extensive simulation results on
random graphs for both of them. These results indicate that, within certain
limits, spanning subgraphs are indeed expected to emerge that perform well in
respect to all requirements. We also discuss the spanning subgraphs' inherent
resilience to failures and adaptability to topological changes
Resilient Wireless Sensor Networks Using Topology Control: A Review
Wireless sensor networks (WSNs) may be deployed in failure-prone environments, and WSNs nodes easily fail due to unreliable wireless connections, malicious attacks and resource-constrained features. Nevertheless, if WSNs can tolerate at most losing k − 1 nodes while the rest of nodes remain connected, the network is called k − connected. k is one of the most important indicators for WSNs’ self-healing capability. Following a WSN design flow, this paper surveys resilience issues from the topology control and multi-path routing point of view. This paper provides a discussion on transmission and failure models, which have an important impact on research results. Afterwards, this paper reviews theoretical results and representative topology control approaches to guarantee WSNs to be k − connected at three different network deployment stages: pre-deployment, post-deployment and re-deployment. Multi-path routing protocols are discussed, and many NP-complete or NP-hard problems regarding topology control are identified. The challenging open issues are discussed at the end. This paper can serve as a guideline to design resilient WSNs
Practical issues for the implementation of survivability and recovery techniques in optical networks
Failure Localization in Power Systems via Tree Partitions
Cascading failures in power systems propagate non-locally, making the control
and mitigation of outages extremely hard. In this work, we use the emerging
concept of the tree partition of transmission networks to provide an analytical
characterization of line failure localizability in transmission systems. Our
results rigorously establish the well perceived intuition in power community
that failures cannot cross bridges, and reveal a finer-grained concept that
encodes more precise information on failure propagations within tree-partition
regions. Specifically, when a non-bridge line is tripped, the impact of this
failure only propagates within well-defined components, which we refer to as
cells, of the tree partition defined by the bridges. In contrast, when a bridge
line is tripped, the impact of this failure propagates globally across the
network, affecting the power flow on all remaining transmission lines. This
characterization suggests that it is possible to improve the system robustness
by temporarily switching off certain transmission lines, so as to create more,
smaller components in the tree partition; thus spatially localizing line
failures and making the grid less vulnerable to large-scale outages. We
illustrate this approach using the IEEE 118-bus test system and demonstrate
that switching off a negligible portion of transmission lines allows the impact
of line failures to be significantly more localized without substantial changes
in line congestion
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