The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory.

Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.

This book constitutes the thoroughly refereed post-conference proceedings of the 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009, held in Piran, Slovenia, in May 2009. The 23 revised full papers presented were carefully reviewed and selected from 53 submissions. The volume also contains two invited papers. SIROCCO addresses topics such as distributed computing, parallel computing, game theory, social networks, networking, mobile computing, peer to peer systems, communication complexity, combinatorial optimization; special focus is put to compact data structures, information dissemination, informative labeling schemes, distributed scheduling, wireless networks and scheduling of transmissions, routing, broadcasting, and localization.

This book constitutes the thoroughly refereed post-conference proceedings of the 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009, held in Piran, Slovenia, in May 2009. The 23 revised full papers presented were carefully reviewed and selected from 53 submissions. The volume also contains two invited papers. SIROCCO addresses topics such as distributed computing, parallel computing, game theory, social networks, networking, mobile computing, peer to peer systems, communication complexity, combinatorial optimization; special focus is put to compact data structures, information dissemination, informative labeling schemes, distributed scheduling, wireless networks and scheduling of transmissions, routing, broadcasting, and localization.