93,769 research outputs found
FLEET: Butterfly Estimation from a Bipartite Graph Stream
We consider space-efficient single-pass estimation of the number of
butterflies, a fundamental bipartite graph motif, from a massive bipartite
graph stream where each edge represents a connection between entities in two
different partitions. We present a space lower bound for any streaming
algorithm that can estimate the number of butterflies accurately, as well as
FLEET, a suite of algorithms for accurately estimating the number of
butterflies in the graph stream. Estimates returned by the algorithms come with
provable guarantees on the approximation error, and experiments show good
tradeoffs between the space used and the accuracy of approximation. We also
present space-efficient algorithms for estimating the number of butterflies
within a sliding window of the most recent elements in the stream. While there
is a significant body of work on counting subgraphs such as triangles in a
unipartite graph stream, our work seems to be one of the few to tackle the case
of bipartite graph streams.Comment: This is the author's version of the work. It is posted here by
permission of ACM for your personal use. Not for redistribution. The
definitive version was published in Seyed-Vahid Sanei-Mehri, Yu Zhang, Ahmet
Erdem Sariyuce and Srikanta Tirthapura. "FLEET: Butterfly Estimation from a
Bipartite Graph Stream". The 28th ACM International Conference on Information
and Knowledge Managemen
On Counting Triangles through Edge Sampling in Large Dynamic Graphs
Traditional frameworks for dynamic graphs have relied on processing only the
stream of edges added into or deleted from an evolving graph, but not any
additional related information such as the degrees or neighbor lists of nodes
incident to the edges. In this paper, we propose a new edge sampling framework
for big-graph analytics in dynamic graphs which enhances the traditional model
by enabling the use of additional related information. To demonstrate the
advantages of this framework, we present a new sampling algorithm, called Edge
Sample and Discard (ESD). It generates an unbiased estimate of the total number
of triangles, which can be continuously updated in response to both edge
additions and deletions. We provide a comparative analysis of the performance
of ESD against two current state-of-the-art algorithms in terms of accuracy and
complexity. The results of the experiments performed on real graphs show that,
with the help of the neighborhood information of the sampled edges, the
accuracy achieved by our algorithm is substantially better. We also
characterize the impact of properties of the graph on the performance of our
algorithm by testing on several Barabasi-Albert graphs.Comment: A short version of this article appeared in Proceedings of the 2017
IEEE/ACM International Conference on Advances in Social Networks Analysis and
Mining (ASONAM 2017
Motif counting beyond five nodes
Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets
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