A Fast Parallel Maximum Clique Algorithm for Large Sparse Graphs and Temporal Strong Components by Ryan A. Rossi, David F. Gleich, Assefaw H. Gebremedhin, Md. Mostofa Ali Patwary.
We propose a fast, parallel, maximum clique algorithm for large, sparse graphs that is designed to exploit characteristics of social and information networks. We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices. In a test with a 1.8 billion-edge social network, the algorithm finds the largest clique in about 20 minutes. For social networks, in particular, we found that using the core number of a vertex in combination with a good heuristic clique finder efficiently removes the vast majority of the search space. In addition, we parallelize the exploration of the search tree. In the algorithm, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes. We use this clique finder to investigate the size of the largest temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph.
Thirty-two networks are reported in this paper and a promised online appendix as around eighty (80).
The online appendix is live but as of today (March 2, 2013), it has no content.
No matter, the paper should keep you busy for more than a little while.
I am interested in parallel graph processing in general but the concept of communicating “…changes to upper and lower bounds on the size of maximum clique…” seems applicable to “merging” in topic maps.
That is if some set of topics share some common characteristic that exclude them from consideration for merging, why apply the merging test at all?
Will have to think about that.