Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
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
Introduction to Algorithms
Finding and Counting Given Length Cycles (Extended Abstract)
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The WebGraph Framework II: Codes For The World-Wide Web
DCC '04 Proceedings of the Conference on Data Compression
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Structural and algorithmic aspects of massive social networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The webgraph framework I: compression techniques
Proceedings of the 13th international conference on World Wide Web
UbiCrawler: a scalable fully distributed web crawler
Software—Practice & Experience
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Radix sorting with no extra space
ESA'07 Proceedings of the 15th annual European conference on Algorithms
New streaming algorithms for counting triangles in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Efficient algorithms for large-scale local triangle counting
ACM Transactions on Knowledge Discovery from Data (TKDD)
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
RAGE - A rapid graphlet enumerator for large networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
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
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
Top-K structural diversity search in large networks
Proceedings of the VLDB Endowment
Why do simple algorithms for triangle enumeration work in the real world?
Proceedings of the 5th conference on Innovations in theoretical computer science
Enhancing decentralized service discovery in open service-oriented multi-agent systems
Autonomous Agents and Multi-Agent Systems
| Hi-index | 5.23 |
Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which have recently received much attention because of their importance in complex network analysis. Here we provide a detailed survey of proposed main-memory solutions to these problems, in a unified way. We note that previous authors have paid surprisingly little attention to space complexity of main-memory solutions, despite its both fundamental and practical interest. We therefore detail space complexities of known algorithms and discuss their implications. We also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs. They have the additional advantage of performing better on power-law graphs, which we also detail. We finally show with an experimental study that these two algorithms perform very well in practice, allowing us to handle cases which were previously out of reach.