Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Business applications of data mining
Communications of the ACM - Evolving data mining into solutions for insights
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
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
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
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Biological Data Mining
What is Twitter, a social network or a news media?
Proceedings of the 19th international conference on World wide web
Counting triangles and the curse of the last reducer
Proceedings of the 20th international conference on World wide web
Generation and analysis of large synthetic social contact networks
Winter Simulation Conference
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
Finding, counting and listing all triangles in large graphs, an experimental study
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
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
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Massive networks arising in numerous application areas poses significant challenges for network analysts as these networks grow to billions of nodes and are prohibitively large to fit in the main memory. Finding the number of triangles in a network is an important problem in the analysis of complex networks. Several interesting graph mining applications depend on the number of triangles in the graph. In this paper, we present an efficient MPI-based distributed memory parallel algorithm, called PATRIC, for counting triangles in massive networks. PATRIC scales well to networks with billions of nodes and can compute the exact number of triangles in a network with one billion nodes and 10 billion edges in 16 minutes. Balancing computational loads among processors for a graph problem like counting triangles is a challenging issue. We present and analyze several schemes for balancing load among processors for the triangle counting problem. These schemes achieve very good load balancing. We also show how our parallel algorithm can adapt an existing edge sparsification technique to approximate the number of triangles with very high accuracy. This modification allows us to count triangles in even larger networks.