Lower Bounds in Communication Complexity

In the thirty years since its inception, communication complexity has become a vital area of theoretical computer science. The applicability of communication complexity to other areas, including circuit and formula complexity, VLSI design, proof complexity, and streaming algorithms, has meant it has attracted a lot of interest. Lower Bounds in Communication Complexity focuses on showing lower bounds on the communication complexity of explicit functions. It treats different variants of communication complexity, including randomized, quantum, and multiparty models. Many tools have been developed for this purpose from a diverse set of fields including linear algebra, Fourier analysis, and information theory. As is often the case in complexity theory, demonstrating a lower bound is usually the more difficult task. The book describes a three-step approach for the development and application of these techniques. This approach can be applied in much the same way for different models, be they randomized, quantum, or multiparty. It is an ideal primer for anyone with an interest in this current and popular topic.