Arboricity and subgraph listing algorithms
SIAM Journal on Computing
The input/output complexity of sorting and related problems
Communications of the ACM
Main-memory triangle computations for very large (sparse (power-law)) graphs
Theoretical Computer Science
Graph Twiddling in a MapReduce World
Computing in Science and Engineering
The h-Index of a Graph and Its Application to Dynamic Subgraph Statistics
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
On triangulation-based dense neighborhood graph discovery
Proceedings of the VLDB Endowment
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Privacy-preserving social network publication against friendship attacks
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Finding maximal cliques in massive networks
ACM Transactions on Database Systems (TODS)
gSketch: on query estimation in graph streams
Proceedings of the VLDB Endowment
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
Arboricity, h-index, and dynamic algorithms
Theoretical Computer Science
Efficient external-memory bisimulation on DAGs
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Truss decomposition in massive networks
Proceedings of the VLDB Endowment
Triangle listing in massive networks
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on the Best of SIGKDD 2011
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
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This paper studies I/O-efficient algorithms for settling the classic triangle listing problem, whose solution is a basic operator in dealing with many other graph problems. Specifically, given an undirected graph G, the objective of triangle listing is to find all the cliques involving 3 vertices in G. The problem has been well studied in internal memory, but remains an urgent difficult challenge when G does not fit in memory, rendering any algorithm to entail frequent I/O accesses. Although previous research has attempted to tackle the challenge, the state-of-the-art solutions rely on a set of crippling assumptions to guarantee good performance. Motivated by this, we develop a new algorithm that is provably I/O and CPU efficient at the same time, without making any assumption on the input G at all. The algorithm uses ideas drastically different from all the previous approaches, and outperformed the existing competitors by a factor over an order of magnitude in our extensive experimentation.