Extensions and refinements of stabilization

Self-stabilizing system is a concept of fault-tolerance in distributed computing. A distributed algorithm is self-stabilizing if, starting from an arbitrary state, it is guaranteed to converge to a legal state in a finite number of states and remains in a legal set of states thereafter. The property of self-stabilization enables a distributed algorithm to recover from a transient fault regardless of its objective. Moreover, a self-stabilizing algorithm does not have to be initialized as it eventually starts to behave correctly. In this thesis, we focus on extensions and refinements of self-stabilization by studying two non-traditional aspects of self-stabilization. In traditional self-stabilizing distributed systems [15], the inherent assumption is that all processes run predefined programs mandated by an external agency which is the owner or the administrator of the entire system. The model works fine for solving problems when processes cooperate with one another, with a global goal. In modern times it is quite common to have a distributed system spanning over multiple administrative domains, and processes have selfish motives to optimize their own payoff. Maximizing individual payoffs under the umbrella of stabilization characterizes the notion of selfish stabilization. We investigate the impact of selfishness on the existence of stabilizing solutions to specific problems in this thesis. Our model of selfishness centers on a graph where the set of nodes is divided into subsets of distinct colors, each having their own