Approximate counting of cycles in streams

Authors:
Madhusudan Manjunath;Kurt Mehlhorn;Konstantinos Panagiotou;He Sun
Affiliations:
Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany and Fudan University, Shanghai, China
Venue:
ESA'11 Proceedings of the 19th European conference on Algorithms
Year:
2011

Citing 10
Cited 4

A Monte-Carlo algorithm for estimating the permanent

SIAM Journal on 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
Clifford algebras and approximating the permanent

Journal of Computer and System Sciences - STOC 2002
The Parameterized Complexity of Counting Problems

SIAM Journal on Computing
Counting triangles in data streams

Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data streams: algorithms and applications

Foundations and Trends® in Theoretical Computer Science
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
Mining Large Networks with Subgraph Counting

ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Estimating clustering indexes in data streams

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

Streaming and communication complexity of clique approximation

ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Counting arbitrary subgraphs in data streams

ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Parallel triangle counting in massive streaming graphs

Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Counting and sampling triangles from a graph stream

Proceedings of the VLDB Endowment

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the subgraph counting problem in data streams and develop the first non-trivial algorithm for approximately counting cycles of an arbitrary but fixed size. Previous non-trivial algorithms could only approximate the number of occurrences of subgraphs of size up to six. Our algorithm is based on the idea of computing instances of complex-valued random variables over the given stream and improves drastically upon the naïve sampling algorithm. In contrast to most existing approaches, our algorithm works in a distributed setting and for the turnstile model, i. e., the input stream is a sequence of edge insertions and deletions.