Problem 11: Counting Triangles

From Open Problems in Sublinear Algorithms
Revision as of 04:12, 28 April 2017 by Krzysztof Onak (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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

Ahn, Guha, and McGregor [AhnGM-12b] proposed an algorithm for streams with both insertions and deletions. It matches the best known bounds for insertion-only streaming algorithms [BuriolFLMS-06].