Dynamic Graph Algorithms Using Dynamic Forest Techniques

A dynamic graph problem is a problem of maintaining a graph subject to edge insertions and/or deletions, and queries about some property of the graph. An incremental dynamic graph algorithm supports just edge insertions, a decremental dynamic graph algorithm supports just edge deletions, and a fully dynamic graph algorithm supports both edge insertions and deletions. In this paper, we survey some of the currently best results in dynamic graph algorithms, first describing the dynamic forest data structures used, then describing the high-level techniques used and presenting an amortized analysis. Then, we discuss some open conjectures about whether the results described in this paper could be generalized.