Small summaries for big data The massive volume of data generated in modern applications can overwhelm our ability to conveniently transmit store and index it. For many scenarios building a compact summary of a dataset that is vastly smaller enables flexibility and efficiency in a range of queries over the data in exchange for some approximation. This comprehensive introduction to data summarization aimed at practitioners and students showcases the algorithms their behavior and the mathematical underpinnings of their operation. The coverage starts with simple sums and approximate counts building to more advanced probabilistic structures such as the Bloom filter distinct value summaries sketches and quantile summaries. Summaries are described for specific types of data such as geometric data graphs and vectors and matrices. The authors offer detailed descriptions of and pseudocode for key algorithms that have been incorporated in systems from companies such as Google Apple Microsoft Netflix and Twitter. graham cormode is Professor of Computer Science at the University of Warwick doing research in data management privacy and big data analysis. Previously he was a principal member of technical staff at AT&T Labs Research. His work has attracted more than 14 000 citations and has appeared in more than 100 conference papers and 40 journal papers and been awarded 30 US patents. Cormode is the corecipient of the 2017 Adams Prize for Mathematics for his work on statistical analysis of big data. He has edited two books on applications of algorithms and coauthored a third. ke yi is a professor in the Department of Computer Science and Engineering Hong Kong University of Science and Technology. He obtained his PhD from Duke University. His research spans theoretical computer science and database systems. He has received the SIGMOD Best Paper Award (2016) a SIGMOD Best Demonstration Award (2015) and a Google Faculty Research Award (2010). He currently serves as an associate editor of ACM Transactions on Database Systems and has also previously served for IEEE Transactions on Knowledge and Data Engineering