Adaptive distributed sorting

The paper presents a fault tolerant distributed sorting algorithm designed to operate in a network with a tree topology subject to transient faults, crashes and joins of both links and nodes. The distributed sorting problem can be informally described as follows: nodes cooperate to reach a global configuration, where every node, depending on its id, is assigned a specific final value taken from the set of the original values across all nodes. Each node has a initial non-corruptible id and value. Fault tolerance 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 safe legitimate states through embedding fault tolerance without the need to recur to explicit exception handlers or backward recovery. Our solution is based on continuous information flow to provide each node with a consistent view of the system state. It requires the knowledge of n, the number of nodes in the system, in order to correctly stabilize and it has O(d) time complexity and O(n) memory requirement where d is the diameter of the tree network. The algorithm handles transient faults by weeding out false information in the system. Nodes can start with completely false information concerning the values, ids and final values in the system, yet the intended behavior is still achieved. Also, nodes and links are allowed to crash, provided the network remains connected. Additionally, new nodes and links can join at any time