Efficient Self-stabilizing Algorithms for Tree Networks

Many proposed self-stabilizing algorithms require an exponential number of moves before stabilizing on a global solution, including some rooting algorithms for tree networks [1, 2, 3]. These results are vastly improved upon in [5] with tree rooting algorithms that require only O(n3 + n2 · ch) moves, where n is the number of nodes in the network and ch is the highest initial value of a variable. In the current paper, we describe a new set of tree rooting algorithms that brings the complexity down to O(n2) moves. This not only reduces the first term by an order of magnitude, but also reduces the second term by an unbounded factor. We further show a generic mapping that can be used to instantiate an efficient self-stabilizing tree algorithm from any traditional sequential tree algorithm that makes a single bottom-up pass through a rooted tree. The new generic mapping improves on the complexity of the technique presented in [7].