Communication comlexity and parallel computing

The communication complexity of two-party protocols, a relatively new measure in complexity theory, has quickly become a fundamental aspect of the field. Similar to Kolmogorov complexity in sequential computations, it serves as a method for analyzing the complexity of problems in parallel information processing. This measure is particularly useful for establishing lower bounds that indicate the necessary computer resources—such as time, hardware, and memory size—required to solve specific tasks. These lower bounds not only help in assessing the computational difficulty of problems but also in validating the optimality of existing algorithms. Furthermore, understanding the communication complexity of a problem can aid in the search for efficient algorithms. As a distinct area within complexity theory, communication complexity is closely linked to several essential complexity measures and contributes to our understanding of determinism, nondeterminism, and randomness in algorithms. A robust mathematical framework has already been developed to address the communication complexity of various computing problems, suggesting that this approach may play a crucial role in tackling several significant open problems in contemporary complexity theory.