### On Dynamic Breadth-First Search in External-Memory

Ulrich Meyer
We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and $O(n)$ edges and monotone update sequences of either $Theta(n)$ edge insertions or $Theta(n)$ edge deletions, we prove an amortized high-probability bound of $O(n/B^{2/3}+sort(n)cdot log B)$ I/Os per update. In contrast, the currently best approach for static BFS on sparse undirected graphs requires $Omega(n/B^{1/2}+sort(n))$ I/Os.