SELF-STABILIZING DISTRIBUTED SORTING IN TREE NETWORKS

Abstract

This paper presents a self-stabilizing distributed sorting algorithm for tree networks. The distributed sorting problem can be informally described as follows: Nodes cooperate to reach a global configuration where every node, depending on its identifier, is assigned a specific final value taken from a set of input values distributed across all nodes. The input values may change in time. In our solution, the system reaches its final configuration in a finite time after the input values are stable and the faults cease. The fault-tolerance and the adaptivity to changing input is achieved using Dijkstra's paradigm of self-stabilization. A self-stabilizing algorithm, regardless of the initial system state, will converge in finite time to a set of legitimate states without the need for explicit exception handlers or backward recovery. Our solution is based on a continuous broadcast with acknowledgment along the tree edges to achieve the synchronization among processes in the system. It has 0(n ×h) time complexity and only 0(log(n) × ) memory requirement where h is the degree of the tree and h is the height of the tree.