Stochastic Matching Problem

Altarelli, Fabrizio; Braunstein, Alfredo; Ramezanpour, Abolfazl; Zecchina, Riccardo

doi:10.1103/physrevlett.106.190601

Cited by 26 publications

(40 citation statements)

References 17 publications

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“…A pivotal role in this respect has been played by a paper by Liu et al [6], in which the problem of finding the minimal set of driver nodes necessary to control a network was mapped into a maximum matching problem. Using a well established statistical mechanics approach [22][23][24][25][26][27], Liu et al [6] characterize in detail the set of driver nodes for real networks and for ensembles of networks with given in-degree and out-degree distribution. By analyzing scale-free networks with minimum in-degree and minimum out-degree equal to 1 they have found that the smaller is the power-law exponent γ of the degree distribution, the larger is the fraction of driver nodes in the network.…”

mentioning

confidence: 99%

Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

2014

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The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the network to the desired dynamical state if an external signal is applied to them. Using the framework of structural controllability, here we show that the density of nodes with in-degree and out-degree equal to 0, 1 and 2 determines the number of driver nodes of random networks. Moreover we show that networks with minimum in-degree and out-degree greater than 2, are always fully controllable by an infinitesimal fraction of driver nodes, regardless on the other properties of the degree distribution. Finally, based on these results, we propose an algorithm to improve the controllability of networks. The controllability of a network [1-10] is a fundamental problem with wide applications ranging from medicine and drug discovery [11], to the characterization of dynamical processes in the brain [12][13][14], or the evaluation of risk in financial markets [15]. While the interplay between the structure of the network [16][17][18][19] and the dynamical processes defined on them has been an active subject of complex network research for more than ten years [20,21], only recently the rich interplay between the controllability of a network and its structure has started to be investigated. A pivotal role in this respect has been played by a paper by Liu et al. [6], in which the problem of finding the minimal set of driver nodes necessary to control a network was mapped into a maximum matching problem. Using a well established statistical mechanics approach [22][23][24][25][26][27], Liu et al. [6] characterize in detail the set of driver nodes for real networks and for ensembles of networks with given in-degree and out-degree distribution. By analyzing scale-free networks with minimum in-degree and minimum out-degree equal to 1 they have found that the smaller is the power-law exponent γ of the degree distribution, the larger is the fraction of driver nodes in the network. This result has prompted the authors of [6] to say that the higher is the heterogeneity of the degree distribution, the less controllable is the network. Later, different papers have addressed questions related to controllability of networks with similar tools [7,28].In this Letter we consider the network controllability and its mapping to the maximum matching problem, exploring the role of low in-degree and low out-degree nodes in the network. We show that by changing the fraction of nodes with in-degree and out-degree less than 3, the number of driver nodes of a network can change in a dramatic way. In particular if the minimum in-degree and the minimum out-degree of a network are both greater than 2 then any network, independently on the level of heterogeneity of the degree distribution, is fully controllable by an infinitesimal fraction of nodes. Therefore we show that the heterogeneity of the network is not the only e...

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confidence: 99%

Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

2014

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“…This is known to be an NP-Hard problem, as proved in [18]. Several approximation factors to this problem are also proposed [2,9].…”

Section: Stochastic Constraint Programming and Related Workmentioning

confidence: 99%

Flow-Based Combinatorial Chance Constraints

Ciré

Çoban

Hoeve

2012

Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems

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Abstract. We study stochastic variants of flow-based global constraints as combinatorial chance constraints. As a specific case study, we focus on the stochastic weighted alldifferent constraint. We first show that determining the consistency of this constraint is NP-hard. We then show how the combinatorial structure of the alldifferent constraint can be used to define chance-based filtering, and to compute a policy. Our propagation algorithm can be extended immediately to related flow-based constraints such as the weighted cardinality constraint. The main benefits of our approach are that our chance-constrained global constraints can be integrated naturally in classical deterministic CP systems, and are more scalable than existing approaches for stochastic constraint programming.

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“…To take into account this uncertainty, we shall work with an objective function which is averaged over the possible outcomes of the observation. More precisely, the above diagnosis problem is a multistage stochastic optimization problem, a subject that has been extensively studied in the optimization community [34,[49][50][51].…”

Section: Problem Statementmentioning

confidence: 99%

“…Our approach is of course computationally more expensive than the previous approaches, but it shows how different types of interactions could be helpful in the course of diagnosis. Additionally, because of recent developments in related fields [32][33][34][35], we now have the necessary concepts and tools to address difficulties in more sophisticated (realistic) problems of this type. This study does not involve usage of real medical data, which is by the way fundamentally incomplete at this moment for such modeling; however, it provides a rationale as to why certain often-neglected statistical information and medical data can be useful in diagnosis and demonstrates that investments in collecting such data will likely pay off.…”

Section: Introductionmentioning

confidence: 99%

Toward First Principle Medical Diagnostics: On the Importance of Disease-Disease and Sign-Sign Interactions

Ramezanpour

Mashaghi

2017

Front. Phys.

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A fundamental problem in medicine and biology is to assign states, e.g., healthy or diseased, to cells, organs or individuals. State assignment or making a diagnosis is often a nontrivial and challenging process and, with the advent of omics technologies, the diagnostic challenge is becoming more and more serious. The challenge lies not only in the increasing number of measured properties and dynamics of the system (e.g., cell or human body) but also in the co-evolution of multiple states and overlapping properties, and degeneracy of states. We develop, from first principles, a generic rational framework for state assignment in cell biology and medicine, and demonstrate its applicability with a few simple theoretical case studies from medical diagnostics. We show how disease-related statistical information can be used to build a comprehensive model that includes the relevant dependencies between clinical and laboratory findings (signs) and diseases. In particular, we include disease-disease and sign-sign interactions and study how one can infer the probability of a disease in a patient with given signs. We perform comparative analysis with simple benchmark models to check the performances of our models. We find that including interactions can significantly change the statistical importance of the signs and diseases. This first principles approach, as we show, facilitates the early diagnosis of disease by taking interactions into accounts, and enables the construction of consensus diagnostic flow charts. Additionally, we envision that our approach will find applications in systems biology, and in particular, in characterizing the phenome via the metabolome, the proteome, the transcriptome, and the genome.

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Stochastic Matching Problem

Cited by 26 publications

References 17 publications

Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

Flow-Based Combinatorial Chance Constraints

Toward First Principle Medical Diagnostics: On the Importance of Disease-Disease and Sign-Sign Interactions

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