Self-stabilizing sorting algorithms

Joseph Chacko, University of Nevada, Las Vegas


A distributed system consists of a set of machines which do not share a global memory. Depending on the connectivity of the network, each machine gets a partial view of the global state. Transient failures in one area of the network may go unnoticed in other areas and may cause the system to go to an illegal global state. However, if the system were self-stabilizing, it would be guaranteed that regardless of the current state, the system would recover to a legal configuration in a finite number of moves; The traditional way of creating reliable systems is to make redundant components. Self-stabilization allows systems to be fault tolerant through software as well. This is an evolving paradigm in the design of robust distributed systems. The ability to recover spontaneously from an arbitrary state makes self-stabilizing systems immune to transient failures or perturbations in the system state such as changes in network topology; This thesis presents an O(nh) fault-tolerant distributed sorting algorithm for a tree network, where n is the number of nodes in the system, and h is the height of the tree. Fault-tolerance is achieved using Dijkstra's paradigm of self-stabilization which is a method of non-masking fault-tolerance embedding the fault-tolerance within the algorithm. Varghese's counter flushing method is used in order to achieve synchronization among processes in the system. In the distributed sorting problem each node is given a value and an id which are non-corruptible. The idea is to have each node take a specific value based on its id. The algorithm handles transient faults by weeding out false information in the system. Nodes can start with completely false information concerning the values and ids of the system yet the intended behavior is still achieved. Also, nodes are allowed to crash and re-enter the system later as well as allowing new nodes to enter the system.