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Reductions in streaming algorithms, with an application to counting triangles in graphs
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Counting triangles in data streams
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ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
DOULION: counting triangles in massive graphs with a coin
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Counting triangles and the curse of the last reducer
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New streaming algorithms for counting triangles in graphs
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Counting arbitrary subgraphs in data streams
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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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
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
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In this note we introduce a new randomized algorithm for counting triangles in graphs. We show that under mild conditions, the estimate of our algorithm is strongly concentrated around the true number of triangles. Specifically, let G be a graph with n vertices, t triangles and let @D be the maximum number of triangles an edge of G is contained in. Our randomized algorithm colors the vertices of G with N=1/p colors uniformly at random, counts monochromatic triangles, i.e., triangles whose vertices have the same color, and scales that count appropriately. We show that if p=max(@Dlognt,lognt) then for any constant @e0 our unbiased estimate T is concentrated around its expectation, i.e., Pr[|T-E[T]|=@eE[T]]=o(1). Finally, our algorithm is amenable to being parallelized. We present a simple MapReduce implementation of our algorithm.