Batch Dynamic Algorithms for Two Graph Problems

We provide a new paradigm to treat insertion and deletion of a batch of edges in a graph, that makes use of the sparsification technique developed for on-line algorithms. In particular, we refer to the problems of minimal spanning forest (MSF), connected components (CC) and k-vertex-connectivity (k-VC). Our batch algorithms, improve of a log-factor over the classical one-by-one algorithms, for k- VC. This improvement is limited to batches of properly “large” size for MSF and CC. In parallel computation we discuss MSF and CC under single edge updating, batch insertions and batch updating, extending the use of the sparsification data structure 10 the CRCVV PRAM model and providing efficient parallel algorithms for these problems (the batch algorithms for CC are indeed work-optimal). We also discuss the difficulty of obtaining a parallel dynamic algorithm for the k-vertex connectivity problem.