# Problem 11: Counting Triangles

Suggested by | Stefano Leonardi |
---|---|

Source | Kanpur 2006 |

Short link | https://sublinear.info/11 |

Given a stream in which edges are inserted and deleted to/from an unweighted, undirected graph, how well can we count triangles and other sub-graphs? Most of the previous work has focused on the case of insertions [BarYossefKS-02,JowhariG-05,BuriolFLMS-06] although it appears that one of the algorithms in [JowhariG-05] may work when edges can be deleted. Is it possible to match the insert-only bounds when edges are inserted and deleted?

## Update

An algorithm for dynamic streams, i.e., when both insertion and deletion of edges are permitted, was proposed in [AhnGM-12b] that matches the best known bounds for insertion-only streaming algorithms [BuriolFLMS-06].