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The identification and counting of small graph patterns, called networkmotifs, is a fundamental primitive in the analysis of networks, withapplication in various domains, from social networks to neuroscience. Severaltechniques have been designed to count the occurrences of motifs in staticnetworks, with recent work focusing on the computational challenges provided bylarge networks. Modern networked datasets contain rich information, such as thetime at which the events modeled by the networks edges happened, which canprovide useful insights into the process modeled by the network. The analysisof motifs in temporal networks, called temporal motifs, is becoming animportant component in the analysis of modern networked datasets. Severalmethods have been recently designed to count the number of instances oftemporal motifs in temporal networks, which is even more challenging than itscounterpart for static networks. Such methods are either exact, and notapplicable to large networks, or approximate, but provide only weak guaranteeson the estimates they produce and do not scale to very large networks. In thiswork we present an efficient and scalable algorithm to obtain rigorousapproximations of the count of temporal motifs. Our algorithm is based on asimple but effective sampling approach, which renders our algorithm practicalfor very large datasets. Our extensive experimental evaluation shows that ouralgorithm provides estimates of temporal motif counts which are more accuratethan the state-of-the-art sampling algorithms, with significantly lower runningtime than exact approaches, enabling the study of temporal motifs, of sizelarger than the ones considered in previous works, on billion edges networks.

PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts