Fully Dynamic Maintenance of Optimum Directed Spanning Forests

We present and analyze a fully dynamic algorithm for maintaining minimum cost directed spanning forests (branchings) in the presence of arc deletions and insertions. We provide algorithms that maintain a data structure, when an arc is deleted from or inserted in the digraph. Queries to the data structure for the optimum branching are answered in O(n) time, while the cost of an optimum branching is always available in optimal worst case time. This work finds application in maintaining a minimum cost multicasting tree in P2P systems as much as in QoS routing in presence of network link failures, recoveries, and load changes.