Faster methods for random sampling
Communications of the ACM
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Finding a minimum circuit in a graph
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Counting triangles in data streams
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
Google's MapReduce programming model – Revisited
Science of Computer Programming
Efficient semi-streaming algorithms for local triangle counting in massive graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Main-memory triangle computations for very large (sparse (power-law)) graphs
Theoretical Computer Science
Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Spectral Counting of Triangles in Power-Law Networks via Element-Wise Sparsification
ASONAM '09 Proceedings of the 2009 International Conference on Advances in Social Network Analysis and Mining
New streaming algorithms for counting triangles in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Proceedings of the 19th international conference on World wide web
A model of computation for MapReduce
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Clustering coefficient queries on massive dynamic social networks
WAIM'10 Proceedings of the 11th international conference on Web-age information management
HADI: Mining Radii of Large Graphs
ACM Transactions on Knowledge Discovery from Data (TKDD)
Proceedings of the 14th International Conference on Extending Database Technology
Counting triangles and the curse of the last reducer
Proceedings of the 20th international conference on World wide web
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Structural trend analysis for online social networks
Proceedings of the VLDB Endowment
Spectral analysis for billion-scale graphs: discoveries and implementation
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part II
Improved sampling for triangle counting with MapReduce
ICHIT'11 Proceedings of the 5th international conference on Convergence and hybrid information technology
An implementation framework of mapreduce email social network analysis
Proceedings of the 6th ACM workshop on Wireless multimedia networking and computing
Concentration and moment inequalities for polynomials of independent random variables
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
Space-round tradeoffs for MapReduce computations
Proceedings of the 26th ACM international conference on Supercomputing
Triangle listing in massive networks
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on the Best of SIGKDD 2011
GRAFT: an approximate graphlet counting algorithm for large graph analysis
Proceedings of the 21st ACM international conference on Information and knowledge management
An effective and efficient parallel approach for random graph generation over GPUs
Journal of Parallel and Distributed Computing
On the streaming complexity of computing local clustering coefficients
Proceedings of the sixth ACM international conference on Web search and data mining
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
A space efficient streaming algorithm for triangle counting using the birthday paradox
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
PATRIC: a parallel algorithm for counting triangles in massive networks
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
An efficient MapReduce algorithm for counting triangles in a very large graph
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Parallel triangle counting in massive streaming graphs
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
How hard is counting triangles in the streaming model?
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
PLASMA-HD: probing the lattice structure and makeup of high-dimensional data
Proceedings of the VLDB Endowment
Counting and sampling triangles from a graph stream
Proceedings of the VLDB Endowment
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Counting the number of triangles in a graph is a beautiful algorithmic problem which has gained importance over the last years due to its significant role in complex network analysis. Metrics frequently computed such as the clustering coefficient and the transitivity ratio involve the execution of a triangle counting algorithm. Furthermore, several interesting graph mining applications rely on computing the number of triangles in the graph of interest. In this paper, we focus on the problem of counting triangles in a graph. We propose a practical method, out of which all triangle counting algorithms can potentially benefit. Using a straightforward triangle counting algorithm as a black box, we performed 166 experiments on real-world networks and on synthetic datasets as well, where we show that our method works with high accuracy, typically more than 99% and gives significant speedups, resulting in even ≈ 130 times faster performance.