72,558 research outputs found
An efficient algorithm for computing exact system and survival signatures of K-terminal network reliability
An efficient algorithm is presented for computing exact system and survival signatures of K-terminal reliability in undirected networks with unreliable edges. K-terminal reliability is defined as the probability that a subset K of the network nodes can communicate with each other. Signatures have several advantages over direct reliability calculation such as enabling certain stochastic comparisons of reliability between competing network topology designs, extremely fast repeat computation of network reliability for different edge reliabilities and computation of network reliability when failures of edges are exchangeable but not independent. Existing methods for computation of signatures for K-terminal network reliability require derivation of cut-sets or path-sets which is only feasible for small networks due to the computational expense. The new algorithm utilises binary decision diagrams, boundary set partition sets and simple array operations to efficiently compute signatures through a factorisation of the network edges. The performance and advantages of the algorithm are demonstrated through application to a set of benchmark networks and a sensor network from an underground mine
Efficient algorithm to study interconnected networks
Interconnected networks have been shown to be much more vulnerable to random
and targeted failures than isolated ones, raising several interesting questions
regarding the identification and mitigation of their risk. The paradigm to
address these questions is the percolation model, where the resilience of the
system is quantified by the dependence of the size of the largest cluster on
the number of failures. Numerically, the major challenge is the identification
of this cluster and the calculation of its size. Here, we propose an efficient
algorithm to tackle this problem. We show that the algorithm scales as O(N log
N), where N is the number of nodes in the network, a significant improvement
compared to O(N^2) for a greedy algorithm, what permits studying much larger
networks. Our new strategy can be applied to any network topology and
distribution of interdependencies, as well as any sequence of failures.Comment: 5 pages, 6 figure
An efficient algorithm for positive realizations
We observe that successive applications of known results from the theory of
positive systems lead to an {\it efficient general algorithm} for positive
realizations of transfer functions. We give two examples to illustrate the
algorithm, one of which complements an earlier result of \cite{large}. Finally,
we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed
efficient in general
Efficient algorithm for optimizing data pattern tomography
We give a detailed account of an efficient search algorithm for the data
pattern tomography proposed by J. Rehacek, D. Mogilevtsev, and Z. Hradil [Phys.
Rev. Lett.~\textbf{105}, 010402 (2010)], where the quantum state of a system is
reconstructed without a priori knowledge about the measuring setup. The method
is especially suited for experiments involving complex detectors, which are
difficult to calibrate and characterize. We illustrate the approach with the
case study of the homodyne detection of a nonclassical photon state.Comment: 5 pages, 5 eps-color figure
Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams
While in many graph mining applications it is crucial to handle a stream of
updates efficiently in terms of {\em both} time and space, not much was known
about achieving such type of algorithm. In this paper we study this issue for a
problem which lies at the core of many graph mining applications called {\em
densest subgraph problem}. We develop an algorithm that achieves time- and
space-efficiency for this problem simultaneously. It is one of the first of its
kind for graph problems to the best of our knowledge.
In a graph , the "density" of a subgraph induced by a subset of
nodes is defined as , where is the set of
edges in with both endpoints in . In the densest subgraph problem, the
goal is to find a subset of nodes that maximizes the density of the
corresponding induced subgraph. For any , we present a dynamic
algorithm that, with high probability, maintains a -approximation
to the densest subgraph problem under a sequence of edge insertions and
deletions in a graph with nodes. It uses space, and has an
amortized update time of and a query time of . Here,
hides a O(\poly\log_{1+\epsilon} n) term. The approximation ratio
can be improved to at the cost of increasing the query time to
. It can be extended to a -approximation
sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm
is the first streaming algorithm that can maintain the densest subgraph in {\em
one pass}. The previously best algorithm in this setting required
passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our
algorithm is tight up to a polylogarithmic factor.Comment: A preliminary version of this paper appeared in STOC 201
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