Review of Communication Complexity and Applications by Anup Rao and Amir Yehudayoff

Abstract

At its core, communication complexity is the study of the amount of information two parties need to exchange in order to compute a function. For instance, Alice receives a string of characters, Bob receives another, and they should decide whether these strings are the same with as few rounds of communication as possible. Multiple settings are conceivable, for instance with multiple parties or with randomness. Upper and lower bounds for communication problems rely on a wealth of mathematical tools, from probability theory to Ramsey theory, making this a complete and exciting topic. Further, communication complexity finds applications in different aspects of theoretical computer science, including circuit complexity and data structures. This usually requires to take a "communication" view of a problem, which in itself can be an eye-opening vantage point.