252 research outputs found
Computational complexity of impact size estimation forspreading processes on networks
Spreading processes on networks are often analyzed to understand how the outcome of the process (e.g. the number of affected nodes) depends on structural properties of the underlying network. Most available results are ensemble averages over certain interesting graph classes such as random graphs or graphs with a particular degree distributions. In this paper, we focus instead on determining the expected spreading size and the probability of large spreadings for a single (but arbitrary) given network and study the computational complexity of these problems using reductions from well-known network reliability problems. We show that computing both quantities exactly is intractable, but that the expected spreading size can be efficiently approximated with Monte Carlo sampling. When nodes are weighted to reflect their importance, the problem becomes as hard as the s-t reliability problem, which is not known to yield an efficient randomized approximation scheme up to now. Finally, we give a formal complexity-theoretic argument why there is most likely no randomized constant-factor approximation for the probability of large spreadings, even for the unweighted case. A hybrid Monte Carlo sampling algorithm is proposed that resorts to specialized s-t reliability algorithms for accurately estimating the infection probability of those nodes that are rarely affected by the spreading proces
Computing the probability mass function of the maximum flow through a reliable network
In this paper we propose a fast state-space enumeration based algorithm called TOP-DOWN capable of computing the probability mass function of the maximum s-t flow through reliable networks. The algorithm computes the probability mass function in the decreasing order of maximum s-t flow values in the network states. This order of enumeration makes this algorithm attractive for commonly observed reliable networks, e.g., in telecommunication networks where link reliabilities are high. We compare the performance of the TOP-DOWN algorithm with a path-based exact algorithm and show that the TOP-DOWN algorithm solves problem much faster and is able to handle much larger problems than existing algorithms.
Link Prediction in Complex Networks: A Survey
Link prediction in complex networks has attracted increasing attention from
both physical and computer science communities. The algorithms can be used to
extract missing information, identify spurious interactions, evaluate network
evolving mechanisms, and so on. This article summaries recent progress about
link prediction algorithms, emphasizing on the contributions from physical
perspectives and approaches, such as the random-walk-based methods and the
maximum likelihood methods. We also introduce three typical applications:
reconstruction of networks, evaluation of network evolving mechanism and
classification of partially labelled networks. Finally, we introduce some
applications and outline future challenges of link prediction algorithms.Comment: 44 pages, 5 figure
A simulation Method for Network Performability Estimation using Heuristically-computed Pathsets and Cutsets
Consider a set of terminal nodes K that belong to a network whose nodes are
connected by links that fail independently with known probabilities. We
introduce a method for estimating any performability measure that depends on
the hop distance between terminal nodes. It generalises previously introduced
Monte Carlo methods for estimation of the K-reliability of networks with
variance reduction compared to crude Monte Carlo. They are based on using sets
of edges named d-pathsets and d-cutsets for reducing the variance of the
estimator. These sets of edges, considered as a priori known in previous
literature, heaviliy affect the attained performance; we hereby introduce and
compare a family of heuristics for their selection. Numerical examples are
presented, showing the significant efficiency improvements that can be obtained
by chaining the edge set selection heuristics to the proposed Monte Carlo
sampling plan
Health-aware economic MPC for operational management of flow-based networks using bayesian networks
This paper presents a health-aware economic Model Predictive Control (EMPC) approach for the Prognostics and Health Management (PHM) of generalized flow-based networks. The proposed approach consists of the integration of the network reliability model obtained from a Bayesian network in the control model. The controller is then able to optimally manage the supply taking into consideration the distribution of the control effort, to extend the life of the actuators by delaying the network reliability decay as much as possible. It also considers an optimal inventory replenishment policy based on a desired risk acceptability level, leading to the availability of safety stocks for unexpected excess demand in networks. The proposed implementation is illustrated with a real case study corresponding to an aggregate model of the Drinking Water transport Network (DWN) of Barcelona.Peer ReviewedPostprint (published version
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