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11
Robust submodular observation selection
, 2008
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations wh ..."
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Cited by 44 (4 self)
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In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating nonunit observation cost or communication and path costs). We also show how the algorithm can be used to nearoptimally trade off expectedcase (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worstcase (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several realworld problems. For Gaussian Process regression, our algorithm compares favorably with stateoftheart heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDPbased algorithms.
Minmax and minmax regret versions of combinatorial optimization problems: A survey
 European Journal of Operational Research
"... Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spannin ..."
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Cited by 23 (1 self)
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Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min st cut, knapsack. Since most of these problems are NPhard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.
Planning for disruptions in supply chain networks
 TutORials in Operations Research. INFORMS
, 2006
"... Abstract Recent events have highlighted the need for planners to consider the risk of disruptions when designing supply chain networks. Supply chain disruptions have a number of causes and may take a number of forms. Once a disruption occurs, there is very little recourse regarding supply chain infr ..."
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Cited by 11 (3 self)
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Abstract Recent events have highlighted the need for planners to consider the risk of disruptions when designing supply chain networks. Supply chain disruptions have a number of causes and may take a number of forms. Once a disruption occurs, there is very little recourse regarding supply chain infrastructure because these strategic decisions cannot be changed quickly. Therefore, it is critical to account for disruptions during the design of supply chain networks so that they perform well even after a disruption. Indeed, these systems can often be made substantially more reliable with only small additional investments in infrastructure. Planners have a range of options available to them in designing resilient supply chain networks, and their choice of approaches will depend on the financial resources available, the decision maker’s risk preference, the type of network under consideration, and other factors. In this tutorial, we present a broad range of models for designing supply chains resilient to disruptions. We first categorize these models by the status of the existing network: A network may be designed from scratch, or an existing network may be modified to prevent disruptions at some facilities. We next divide each category based on the underlying optimization model (facility location or network design) and the risk measure (expected cost or worstcase cost).
Adaptive Coarse Space Selection in the BDDC and the FETIDP Iterative Substructuring Methods: Optimal Face Degrees of Freedom
"... We propose adaptive selection of the coarse space of the BDDC and FETIDP iterative substructuring methods by adding coarse degrees of freedom (dofs) on faces between substructures constructed using eigenvectors associated with the faces. Provably the minimal number of coarse dofs on the faces is ad ..."
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Cited by 9 (3 self)
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We propose adaptive selection of the coarse space of the BDDC and FETIDP iterative substructuring methods by adding coarse degrees of freedom (dofs) on faces between substructures constructed using eigenvectors associated with the faces. Provably the minimal number of coarse dofs on the faces is added to decrease the condition number estimate under a target value specified a priori. It is assumed that corner dofs are already sufficient to prevent relative rigid body motions of any two substructures with a common face. It is shown numerically on a 2D elasticity problem that the condition number estimate based on faces is quite indicative of the actual condition number and that the method can select adaptively a hard part of the problem and concentrate computational work there to achieve the target value for the condition number and good convergence of the iterations, at a modest cost.
A Semimartingale Approach For Modeling Multiphase Flow In Heterogeneous Porous Media
, 2005
"... This paper is a followup to Dean and Russell[2] in which the formulation of our model of NAPL flow in heterogeneous porous media is based on the traditional argument of developing a FokkerPlanck equation for a diffusion process and then modifying this equation to handle the behavior of the fluid p ..."
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Cited by 3 (0 self)
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This paper is a followup to Dean and Russell[2] in which the formulation of our model of NAPL flow in heterogeneous porous media is based on the traditional argument of developing a FokkerPlanck equation for a diffusion process and then modifying this equation to handle the behavior of the fluid particle at an interface between sands of different permeabilities. Since the capillary diffusivity can change significantly across the interface, we call these changes jumps and incorporate them into the stochastic differential equation that describes the motion of the NAPL particle. Since this is a traditional approach that is modified to incorporate nontraditional behavior such as jumps, we call it a bottomup approach. The modified stochastic differential equation can then model pooling and channeling that occurs at such interfaces. In this paper, an attempt is made to accomplish the same result starting with a theory of stochastic processes that allows jumps. We start with semimartingale processes which are càdlàg. Since these processes allow jumps by definition, we call this approach the topdown approach.
Resilient Observation Selection in Adversarial Settings
"... Abstract — Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensorbased pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. Th ..."
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Abstract — Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensorbased pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. This problem is further complicated by the presence of strategic adversaries, who may disable some of the deployed sensors in order to impair the operator’s ability to make predictions. Assuming that the operator employs a Gaussianprocessbased regression model, we formulate the problem of attackresilient sensor placement as the problem of selecting a subset from a set of possible observations, with the goal of minimizing the uncertainty of predictions. We show that both finding an optimal resilient subset and finding an optimal attack against a given subset are NPhard problems. Since both the design and the attack problems are computationally complex, we propose efficient heuristic algorithms for solving them and present theoretical approximability results. Finally, we show that the proposed algorithms perform exceptionally well in practice using numerical results based on realworld datasets. I.
Prepared by Sandia National Laboratories
, 2006
"... Approved for public release; further dissemination unlimited. ..."
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