The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of 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
Counting triangles in data streams
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
Microscopic evolution of social networks
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
New streaming algorithms for counting triangles in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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The problem of (approximately) counting the number of triangles in a graph is one of the basic problems in graph theory. In this paper we study the problem in the streaming model. Specifically, the amount of memory required by a randomized algorithm to solve this problem. In case the algorithm is allowed one pass over the stream, we present a best possible lower bound of Ω(m) for graphs G with m edges. If a constant number of passes is allowed, we show a lower bound of Ω(m/T), T the number of triangles. We match, in some sense, this lower bound with a 2-pass O(m/T1/3)-memory algorithm that solves the problem of distinguishing graphs with no triangles from graphs with at least T triangles. We present a new graph parameter ρ(G) --- the triangle density, and conjecture that the space complexity of the triangles problem is Θ(m/ρ(G)). We match this by a second algorithm that solves the distinguishing problem using O(m/ρ(G))-memory.