A Fast Parallel Maximum Clique Algorithm for Large Sparse Graphs and Temporal Strong Components
@article{Rossi2013AFP, title={A Fast Parallel Maximum Clique Algorithm for Large Sparse Graphs and Temporal Strong Components}, author={Ryan A. Rossi and David F. Gleich and Assefaw Hadish Gebremedhin and Md. Mostofa Ali Patwary}, journal={ArXiv}, year={2013}, volume={abs/1302.6256} }
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…
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References
SHOWING 1-10 OF 62 REFERENCES
Finding maximal cliques in massive networks
- Computer ScienceTODS
- 2011
A general framework enables maximal clique enumeration to be processed recursively in small subgraphs of the input graph, thus allowing in-memory computation of maximal cliques without the costly random disk access.
Fast Algorithms for the Maximum Clique Problem on Massive Sparse Graphs
- Computer ScienceWAW
- 2013
This work presents a new exact algorithm that employs novel pruning techniques and is able to quickly find maximum cliques in large sparse graphs and presents a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions.
A scalable, parallel algorithm for maximal clique enumeration
- Computer ScienceJ. Parallel Distributed Comput.
- 2009
Listing All Maximal Cliques in Large Sparse Real-World Graphs
- Computer ScienceJEAL
- 2013
We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Loffler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our…
Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time
- MathematicsExact Complexity of NP-hard Problems
- 2010
There exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy, and this algorithm matches the Θ(d(n − d)3 d/3) worst-case output size of the problem whenever n − d = Ω(n).
The maximum clique enumeration problem: algorithms, applications, and implementations
- Computer ScienceBMC Bioinformatics
- 2012
Empirical testing reveals crucial but latent features of high-throughput biological data which distinguish real data from random data intended to reproduce salient topological features and novel decomposition strategies are tuned to the data and coupled with the best FPT MCE implementations.
Fast algorithms for maximal clique enumeration with limited memory
- Computer ScienceKDD
- 2012
This work proposes an efficient partition-based algorithm for MCE that addresses the problem of processing large graphs with limited memory and reduces the high cost of CPU computation of MCE by a careful nested partition based on a cost model.
Algorithm 457: finding all cliques of an undirected graph
- Computer Science
- 1973
Two backtracking algorithms are presented, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique, and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed.
Vertex neighborhoods, low conductance cuts, and good seeds for local community methods
- Computer ScienceKDD
- 2012
It is theoretically demonstrate that two commonly observed properties of social networks, heavy-tailed degree distributions and large clustering coefficients, imply the existence of vertex neighborhoods (also known as egonets) that are themselves good communities.
The worst-case time complexity for generating all maximal cliques and computational experiments
- Computer Science, MathematicsTheor. Comput. Sci.
- 2006