Optimal algorithms for the vertex updating problem of a minimum spanning tree

The vertex updating problem for a minimum spanning tree (MST) is defined as follows: Given a graph G=(V,E_G) and its MST T, update T when a new vertex z is introduced along with weighted edges that connect z with the vertices of G. The authors present a set of rules that, together with a valid tree-contraction schedule are used to produce simple optimal parallel algorithms that run in O(log n) parallel time using n/lgn EREW PRAMs where n=|V|. These rules can also be used to derive simple linear-time sequential algorithms for the same problem. It is also shown how this solution can be used to solve the multiple vertex updating problem: Update a given MST when k new vertices are introduced simultaneously. This problem is solved in O(lgk.lgn) parallel time using _lgk.lgn ^k.n EREW PRAM processors