Distributed Matroid Basis Completion via Elimination Upcast and Distributed Correction of Minimum-Weight Spanning Trees

This paper proposes a time-eecient distributed solution for the matroid basis completion problem. The solution is based on a technique called elimination upcast, enabling us to reduce the amount of work necessary for the upcast by relying on the special properties of matroids. As an application, it is shown that the algorithm can be used for correcting a minimum weight spanning tree computed for a D-diameter network, after k edges have changed their weight, in time O(k + D).