Technical Report Number
We present a set of rules that can be used to give optimal solutions to the vertex updating problem for a minimum spanning tree: Update a given MST when a new vertex z is introducted, along with weighted edges that connect z with the vertices of the graph. These rules lead to simple parallel algorithms that run in O(lg n) parallel time using n/lg n EREW PRAMs. They can also be used to derive simple linear-time sequential algorithms for the same problem. Furthermore, we show how our solution can be used to solve the multiple vertex updating problem.
Dartmouth Digital Commons Citation
Johnson, Donald B. and Metaxas, Panagiotis, "Optimal Parallel and Sequential Algorithms for the Vertex Updating Problem of a Minimum Spanning Tree" (1991). Computer Science Technical Report PCS-TR91-159. https://digitalcommons.dartmouth.edu/cs_tr/59