Online failure diagnosis in interdependent networks

Abstract

In interdependent networks, nodes are connected to each other with respect to their failure dependency relations. As a result of this dependency, a failure in one of the nodes of one of the networks within a system of several interdependent networks can cause the failure of the entire system. Diagnosing the initial source of the failure in a collapsed system of interdependent networks is an important problem to be addressed. We study an online failure diagnosis problem defined on a collapsed system of interdependent networks where the source of the failure is at an unknown node (v). In this problem, each node of the system has a positive inspection cost and the source of the failure is diagnosed when v is inspected. The objective is to provide an online algorithm which considers dependency relations between nodes and diagnoses v with minimum total inspection cost. We address this problem from worst-case competitive analysis perspective for the first time. In this approach, solutions which are provided under incomplete information are compared with the best solution that is provided in presence of complete information using the competitive ratio (CR) notion. We give a lower bound of the CR for deterministic online algorithms and prove its tightness by providing an optimal deterministic online algorithm. Furthermore, we provide a lower bound on the expected CR of randomized online algorithms and prove its tightness by presenting an optimal randomized online algorithm. We prove that randomized algorithms are able to obtain better CR compared to deterministic algorithms in the expected sense for this online problem.