A Bilevel Optimization Approach for a Class of Combinatorial Problems with Disruptions and Probing

\(\) We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision-maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which … Read more

Maximum Likelihood Probability Measures over Sets and Applications to Data-Driven Optimization

\(\) Motivated by data-driven approaches to sequential decision-making under uncertainty, we study maximum likelihood estimation of a distribution over a general measurable space when, unlike traditional setups, realizations of the underlying uncertainty are not directly observable but instead are known to lie within observable sets. While extant work studied the special cases when the observed … Read more

Interdicting Low-Diameter Cohesive Subgroups in Large-Scale Social Networks

The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly-knit communities whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this … Read more

Graph Signatures: Identification and Optimization

We introduce a new graph-theoretic paradigm called a graph signature that describes persistent patterns in a sequence of graphs. This framework is motivated by the need to detect subgraphs of significance in temporal networks, e.g., social and biological networks that evolve over time. Because the subgraphs of interest may not all “look alike” in the … Read more