Self-stabilizing leader election in dynamic networks

The leader election problem is one of the fundamental problems in distributed computing. It has applications in almost every domain. In dynamic networks, topology is expected to change frequently. An algorithm A is self-stabilizing if, starting from a completely arbitrary configuration, the network will eventually reach a legitimate configuration. Note that any self-stabilizing algorithm for the leader election problem is also an algorithm for the dynamic leader election problem, since when the topology of the network changes, we can consider that the algorithm is starting over again from an arbitrary state. There are a number of such algorithms in the literature which require large memory in each process, or which take O(n) time to converge, where n is size of the network. Given the need to conserve time, and possibly space, these algorithms may not be practical for the dynamic leader election problem. In this thesis, three silent self-stabilizing asynchronous distributed algorithms are given for the leader election problem in a dynamic network with unique IDs, using the composite model of computation. If topological changes to the network pause, a leader is elected for each component. A BFS tree is also constructed in each component, rooted at the leader. When another topological change occurs, leaders are then elected for the new components. This election takes O (Diam) rounds, where Diam is the maximum diameter of any component. The three algorithms differ in their leadership stability. The first algorithm, which is the fastest in the worst case, chooses an arbitrary process as the leader. The second algorithm chooses the process of highest priority in each component, where priority can be defined in a variety of ways. The third algorithm has the strictest leadership stability; if a component contains processes that were leaders before the topological change, one of those must be elected to be the new leader. Formal algorithms and their correctness proofs will be given

Self-stabilizing k-clustering in mobile ad hoc networks

In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph