Parameterized complexity of graph theoretic problems in fault-tolerant models

Abstract

Fault tolerance is a crucial aspect of modern computing systems, ensuring that systems can continue to operate correctly even in the presence of faults or failures. In the case of graph theoretic problems, this translates to dealing with problems where the structure of the graph is either compromised or unavailable. This covers many applications, such as social networks, transportation services, power distribution systems, and malicious network attacks. We aim to design robust algorithms so that systems maintain their functionalities in the face of such disruptions. We view the problem through the lens of parameterized algorithms, as param eterized complexity provides a more nuanced and rigorous picture of the problem’s difficulty, considering its structure, the types of possible failures, and the structural parameters. This paper presents an analysis of the literature studied so far and their applications to our problems. We aim to explore the relevant materials further and develop novel ideas moving forward.