Pattern counting in graphs is fundamental to several network sci ence tasks, and there is an abundance of scalable methods for estimating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer structure, and incorporating temporal information in particular has become a key part of network analysis. Consequently, temporal motifs, which are generalizations of small subgraph patterns that incorporate temporal ordering on edges, are an emerging part of the network analysis toolbox. However, there are no algorithms for fast estimation of temporal motifs counts; moreover, we show that even counting simple temporal starmore »
Tiered Sampling: An Efficient Method for Counting Sparse Motifs in Massive Graph Streams
We introduce Tiered Sampling , a novel technique for estimating the count of sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs—subgraph patterns—that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of substructures of the desired motif. By storing more frequent substructures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4cliques, we present a method which allows generalizing Tiered Sampling to obtain highquality estimates for the number of more »
 Award ID(s):
 1813444
 Publication Date:
 NSFPAR ID:
 10273679
 Journal Name:
 ACM Transactions on Knowledge Discovery from Data
 Volume:
 15
 Issue:
 5
 Page Range or eLocationID:
 1 to 52
 ISSN:
 15564681
 Sponsoring Org:
 National Science Foundation
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