O(1) Parallel Time Incremental Graph Algorithms

Fast parallel algorithms are presented for updating minimum spanning trees, connected components and bridges of an undirected graph when a minor change is made to the graph such as addition or deletion of a vertex or an edge. The machine model used is a parallel random access machine that allows simultaneous reads as well as simultaneous writes into the same memory location. In the latter case one processor succeeds but we do not know which. The algorithms described in this paper require O(1) time and are efficient when compared to previously known O(logn) time algorithms for initial computation of the above mentioned graph properties on this model. An important feature of our algorithms is their versatility, that is, they can be adapted to run efficiently on all variations of this model with very little modification.