In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the identification of the most central nodes in such networks. Additionally to being massive, modern networks also contain information about the time at which their events occur. Such networks are often called temporal networks. The temporal information makes the study of the betweenness centrality in temporal networks (i.e., temporal betweenness centrality) much more challenging than in static networks (i.e., networks without temporal information). Moreover, the exact computation of the temporal betweenness centrality is often impractical on even moderately-sized networks, given its extremely high computational cost. A natural approach to reduce such computational cost is to obtain high-quality estimates of the exact values of the temporal betweenness centrality. In this work we present , the first sampling-based approximation algorithm for estimating the temporal betweenness centrality values of the nodes in a temporal network, providing rigorous probabilistic guarantees on the quality of its output. is able to compute the estimates of the temporal betweenness centrality values under two different optimality criteria for the shortest paths of the temporal network. In addition, outputs high-quality estimates with sharp theoretical guarantees leveraging on the empirical Bernstein bound, an advanced concentration inequality. Finally, our experimental evaluation shows that significantly reduces the computational resources required by the exact computation of the temporal betweenness centrality on several real world networks, while reporting high-quality estimates with rigorous guarantees.

MOTIVATION: The extraction of k-mers is a fundamental component in many complex analyses of large next-generation sequencing datasets, including reads classification in genomics and the characterization of RNA-seq datasets. The extraction of all k-mers and their frequencies is extremely demanding in terms of running time and memory, owing to the size of the data and to the exponential number of k-mers to be considered. However, in several applications, only frequent k-mers, which are k-mers appearing in a relatively high proportion of the data, are required by the analysis. RESULTS: In this work, we present SPRISS, a new efficient algorithm to approximate frequent k-mers and their frequencies in next-generation sequencing data. SPRISS uses a simple yet powerful reads sampling scheme, which allows to extract a representative subset of the dataset that can be used, in combination with any k-mer counting algorithm, to perform downstream analyses in a fraction of the time required by the analysis of the whole data, while obtaining comparable answers. Our extensive experimental evaluation demonstrates the efficiency and accuracy of SPRISS in approximating frequent k-mers, and shows that it can be used in various scenarios, such as the comparison of metagenomic datasets, the identification of discriminative k-mers, and SNP (single nucleotide polymorphism) genotyping, to extract insights in a fraction of the time required by the analysis of the whole dataset. AVAILABILITY AND IMPLEMENTATION: SPRISS [a preliminary version (Santoro et al., 2021) of this work was presented at RECOMB 2021] is available at https://github.com/VandinLab/SPRISS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.