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ABSTRACT Evacuation plans are designed to move people to safety in case of a disaster. It mainly consists of two components: routing and scheduling. Joint optimization of these two components with the goal of minimizing total evacuation time is a computationally hard problem, specifically when the problem instance is large. Moreover, often in disaster situations, there is uncertainty regarding the passability of roads throughout the evacuation time period. In this paper, we present a way to model the time-varying risk associated with roads in disaster situations. We also design a heuristic method based on the well known Large Neighborhood Search framework to perform the joint optimization task. We use real-world road network and population data from Harris County in Houston, Texas and apply our heuristic to find evacuation routes and schedules for the area. We show that the proposed method is able to find good solutions within a reasonable amount of time. We also perform agent-based simulations of the evacuation using these solutions to evaluate their quality and efficacy. 

In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods. 

Graph cut problems are fundamental in combinatorial optimization, and are a central object of study in both theory and practice. Further, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different notions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees. 

ABSTRACT Efficient contact tracing and isolation is an effective strategy to control epidemics, as seen in the Ebola epidemic and COVID-19 pandemic. An important consideration in contact tracing is the budget on the number of individuals asked to quarantine—the budget is limited for socioeconomic reasons (e.g., having a limited number of contact tracers). Here, we present a Markov Decision Process (MDP) framework to formulate the problem of using contact tracing to reduce the size of an outbreak while limiting the number of people quarantined. We formulate each step of the MDP as a combinatorial problem, MinExposed, which we demonstrate is NP-Hard. Next, we develop two approximation algorithms, one based on rounding the solutions of a linear program and another (greedy algorithm) based on choosing nodes with a high (weighted) degree. A key feature of the greedy algorithm is that it does not need complete information of the underlying social contact network, making it implementable in practice. Using simulations over realistic networks, we show how the algorithms can help in bending the epidemic curve with a limited number of isolated individuals. 

Many papers have addressed the problem of learning the behavior (i.e., the local interaction function at each node) of a networked system through active queries, assuming that the network topology is known. We address the problem of inferring both the network topology and the behavior of such a system through active queries. Our results are for systems where the state of each node is from {0, 1} and the local functions are Boolean. We present inference algorithms under both batch and adaptive query models for dynamical systems with symmetric local functions. These algorithms show that the structure and behavior of such dynamical systems can be learnt using only a polynomial number of queries. Further, we establish a lower bound on the number of queries needed to learn such dynamical systems. We also present experimental results obtained by running our algorithms on synthetic and real-world networks. 

Efficient contact tracing and isolation is an effective strategy to control epidemics, as seen in the Ebola epidemic and COVID-19 pandemic. An important consideration in contact tracing is the budget on the number of individuals asked to quarantine—the budget is limited for socioeconomic reasons (e.g., having a limited number of contact tracers). Here, we present a Markov Decision Process (MDP) framework to formulate the problem of using contact tracing to reduce the size of an outbreak while limiting the number of people quarantined. We formulate each step of the MDP as a combinatorial problem, MinExposed, which we demonstrate is NP-Hard. Next, we develop two approximation algorithms, one based on rounding the solutions of a linear program and another (greedy algorithm) based on choosing nodes with a high (weighted) degree. A key feature of the greedy algorithm is that it does not need complete information of the underlying social contact network, making it implementable in practice. Using simulations over realistic networks, we show how the algorithms can help in bending the epidemic curve with a limited number of isolated individuals. 

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinInfEdge problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most B edges; similarly the MinInfNode problem involves removing at most B vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinInfEdge, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation--based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinInfNode problem. 

Vaccination is the primary intervention for controlling the spread of infectious diseases. A certain level of vaccination rate (referred to as “herd immunity”) is needed for this intervention to be effective. However, there are concerns that herd immunity might not be achieved due to an increasing level of hesitancy and opposition to vaccines. One of the primary reasons for this is the cost of non-conformance with one’s peers. We use the framework of network coordination games to study the persistence of anti-vaccine sentiment in a population. We extend it to incorporate the opposing forces of the pressure of conforming to peers, herd-immunity and vaccination benefits. We study the structure of the equilibria in such games, and the characteristics of unvaccinated nodes. We also study Stackelberg strategies to reduce the number of nodes with anti-vaccine sentiment. Finally, we evaluate our results on different kinds of real world social networks. 

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we present PREEMPT, a new approach for intervention via maximizing the influence of vaccinated nodes on the network.We prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for PREEMPT, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that PREEMPT is able to achieve a significant reduction (up to 6:75) in the percentage of people infected and up to 98% reduction in the peak of the infection on a cityscale network. We also show strong scaling results of PREEMPT on up to 128 nodes of the Summit supercomputer. Our parallel implementation is able to significantly reduce time to solution, from hours to minutes on large networks. This work represents a first-of-its-kind effort in parallelizing greedy hill climbing and applying it toward devising effective interventions for epidemics.