Identifying Sources of Anomalies in Complex Networks

The problem of monitoring complex networks for the detection of anomalous behavior is well known. Sensors are usually deployed for the purpose of monitoring these networks for anomalies and Sensor Placement Optimization (SPO) is the problem of determining where these sensors should be placed (deployed) in the network. Prior works have utilized the well known Set Cover formulation in order to determine the locations where sensors should be placed in the network, so that anomalies can be effectively detected. However, such works cannot be utilized to address the problem when the objective is to not only detect the presence of anomalies, but also to detect (distinguish) the source(s) of the detected anomalies, i.e., uniquely monitoring the network. In this dissertation, I attempt to fill in this gap by utilizing the mathematical concept of Identifying Codes and illustrating how it not only can overcome the aforementioned limitation, but also it, and its variants, can be utilized to monitor complex networks modeled from multiple domains. Over the course of this dissertation, I make key contributions which further enhance the efficacy and applicability of Identifying Codes as a monitoring strategy. First, I show how Identifying Codes are superior to not only the Set Cover formulation but also standard graph centrality metrics, for the purpose of uniquely monitoring complex networks. Second, I study novel problems such as the budget constrained Identifying Code, scalable Identifying Code, robust Identifying Code etc., and present algorithms and results for the respective problems. Third, I present useful Identifying Code results for restricted graph classes such as Unit Interval Bigraphs and Unit Disc Bigraphs. Finally, I show the universality of Identifying Codes by applying it to multiple domains.