147,685 research outputs found
Single failure resiliency in greedy routing
Using greedy routing, network nodes forward packets towards neighbors which are closer to their destination. This approach makes greedy routers significantly more memory-efficient than traditional IP-routers using longest-prefix matching. Greedy embeddings map network nodes to coordinates, such that greedy routing always leads to the destination. Prior works showed that using a spanning tree of the network topology, greedy embeddings can be found in different metric spaces for any graph. However, a single link/node failure might affect the greedy embedding and causes the packets to reach a dead end. In order to cope with network failures, existing greedy methods require large resources and cause significant loss in the quality of the routing (stretch loss). We propose efficient recovery techniques which require very limited resources with minor effect on the stretch. As the proposed techniques are protection, the switch-over takes place very fast. Low overhead, simplicity and scalability of the methods make them suitable for large-scale networks. The proposed schemes are validated on large topologies with properties similar to the Internet. The performances of the schemes are compared with an existing alternative referred as gravity pressure routing
High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods
In this paper we consider the task of estimating the non-zero pattern of the
sparse inverse covariance matrix of a zero-mean Gaussian random vector from a
set of iid samples. Note that this is also equivalent to recovering the
underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We
present two novel greedy approaches to solving this problem. The first
estimates the non-zero covariates of the overall inverse covariance matrix
using a series of global forward and backward greedy steps. The second
estimates the neighborhood of each node in the graph separately, again using
greedy forward and backward steps, and combines the intermediate neighborhoods
to form an overall estimate. The principal contribution of this paper is a
rigorous analysis of the sparsistency, or consistency in recovering the
sparsity pattern of the inverse covariance matrix. Surprisingly, we show that
both the local and global greedy methods learn the full structure of the model
with high probability given just samples, which is a
\emph{significant} improvement over state of the art -regularized
Gaussian MLE (Graphical Lasso) that requires samples. Moreover,
the restricted eigenvalue and smoothness conditions imposed by our greedy
methods are much weaker than the strong irrepresentable conditions required by
the -regularization based methods. We corroborate our results with
extensive simulations and examples, comparing our local and global greedy
methods to the -regularized Gaussian MLE as well as the Neighborhood
Greedy method to that of nodewise -regularized linear regression
(Neighborhood Lasso).Comment: Accepted to AI STAT 2012 for Oral Presentatio
Lazier Than Lazy Greedy
Is it possible to maximize a monotone submodular function faster than the
widely used lazy greedy algorithm (also known as accelerated greedy), both in
theory and practice? In this paper, we develop the first linear-time algorithm
for maximizing a general monotone submodular function subject to a cardinality
constraint. We show that our randomized algorithm, STOCHASTIC-GREEDY, can
achieve a approximation guarantee, in expectation, to the
optimum solution in time linear in the size of the data and independent of the
cardinality constraint. We empirically demonstrate the effectiveness of our
algorithm on submodular functions arising in data summarization, including
training large-scale kernel methods, exemplar-based clustering, and sensor
placement. We observe that STOCHASTIC-GREEDY practically achieves the same
utility value as lazy greedy but runs much faster. More surprisingly, we
observe that in many practical scenarios STOCHASTIC-GREEDY does not evaluate
the whole fraction of data points even once and still achieves
indistinguishable results compared to lazy greedy.Comment: In Proc. Conference on Artificial Intelligence (AAAI), 201
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