10,939 research outputs found
Combinatorial optimization in networks with Shared Risk Link Groups
International audienceThe notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the classical graph models: shortest paths, minimum cuts, or pairs of disjoint paths. In the SRLG context, the optimization criterion for these objects is no longer the number of edges they use, but the number of SRLGs involved. Unfortunately, computing these combinatorial objects is NP-hard and hard to approximate with this objective in general. Nevertheless some objects can be computed in polynomial time when the SRLGs satisfy certain structural properties of locality which correspond to practical ones, namely the star property (all links affected by a given SRLG are incident to a unique node) and the span 1 property (the links affected by a given SRLG form a connected component of the network). The star property is defined in a multi-colored model where a link can be affected by several SRLGs while the span property is defined only in a mono-colored model where a link can be affected by at most one SRLG. In this paper, we extend these notions to characterize new cases in which these optimization problems can be solved in polynomial time. We also investigate the computational impact of the transformation from the multi-colored model to the mono-colored one. Experimental results are presented to validate the proposed algorithms and principles
Social Network Based Substance Abuse Prevention via Network Modification (A Preliminary Study)
Substance use and abuse is a significant public health problem in the United
States. Group-based intervention programs offer a promising means of preventing
and reducing substance abuse. While effective, unfortunately, inappropriate
intervention groups can result in an increase in deviant behaviors among
participants, a process known as deviancy training. This paper investigates the
problem of optimizing the social influence related to the deviant behavior via
careful construction of the intervention groups. We propose a Mixed Integer
Optimization formulation that decides on the intervention groups, captures the
impact of the groups on the structure of the social network, and models the
impact of these changes on behavior propagation. In addition, we propose a
scalable hybrid meta-heuristic algorithm that combines Mixed Integer
Programming and Large Neighborhood Search to find near-optimal network
partitions. Our algorithm is packaged in the form of GUIDE, an AI-based
decision aid that recommends intervention groups. Being the first quantitative
decision aid of this kind, GUIDE is able to assist practitioners, in particular
social workers, in three key areas: (a) GUIDE proposes near-optimal solutions
that are shown, via extensive simulations, to significantly improve over the
traditional qualitative practices for forming intervention groups; (b) GUIDE is
able to identify circumstances when an intervention will lead to deviancy
training, thus saving time, money, and effort; (c) GUIDE can evaluate current
strategies of group formation and discard strategies that will lead to deviancy
training. In developing GUIDE, we are primarily interested in substance use
interventions among homeless youth as a high risk and vulnerable population.
GUIDE is developed in collaboration with Urban Peak, a homeless-youth serving
organization in Denver, CO, and is under preparation for deployment
Learning to Discover Sparse Graphical Models
We consider structure discovery of undirected graphical models from
observational data. Inferring likely structures from few examples is a complex
task often requiring the formulation of priors and sophisticated inference
procedures. Popular methods rely on estimating a penalized maximum likelihood
of the precision matrix. However, in these approaches structure recovery is an
indirect consequence of the data-fit term, the penalty can be difficult to
adapt for domain-specific knowledge, and the inference is computationally
demanding. By contrast, it may be easier to generate training samples of data
that arise from graphs with the desired structure properties. We propose here
to leverage this latter source of information as training data to learn a
function, parametrized by a neural network that maps empirical covariance
matrices to estimated graph structures. Learning this function brings two
benefits: it implicitly models the desired structure or sparsity properties to
form suitable priors, and it can be tailored to the specific problem of edge
structure discovery, rather than maximizing data likelihood. Applying this
framework, we find our learnable graph-discovery method trained on synthetic
data generalizes well: identifying relevant edges in both synthetic and real
data, completely unknown at training time. We find that on genetics, brain
imaging, and simulation data we obtain performance generally superior to
analytical methods
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