Stabilizing Graph Algorithms

A distributed system consists of a set of loosely connected processes that do not share a global memory. The task of many open distributed systems is to guarantee an invariance relationship over the states of the system, and the states of the environment influencing that system. When the invariant holds, the state of the system is legal; otherwise it is illegal. Occasionally, the actions of the environment perturbs the state of the system and puts it into an illegal state-this is viewed as a transient failure. A self-stabilizing system guarantees that, regardless of the current state, the system returns to a legal state in a bounded number of steps. Due to this property, self-stabilizing systems can beused to deal with variety of faults in distributed systems. This dissertation deals with devising self-stabilizing distributed systems for a variety of graph theoretic problems. These include graph coloring, center and median finding, and maxima finding problems. The proposed solutions tolerate dynamic changes in the topology of the network.