Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms. Contents Some definitions and notations Ramsey theory Bi-color diagonal classical Ramsey numbers Paley graphs and lower bounds for R(k, k) Bi-color off-diagonal classical Ramsey numbers Multicolor classical Ramsey numbers Generalized Ramsey numbers Folkman numbers The Erdos-Hajnal conjecture Other Ramsey-type problems in graph theory On van der Waerden numbers and Szemeredi's theorem More problems of Ramsey type in additive number theory Sidon-Ramsey numbers Games in Ramsey theory Local Ramsey theory Set-coloring Ramsey theory Other problems and conjectures

Driven by the increasing demand for capacity and Quality of Service in wireless cellular networks and motivated by the distributed antenna system, the authors proposed a cooperative communication architecture-Group Cell architecture, which was initially brought forward in 2001. Years later, Coordinated Multiple-Point Transmission and Reception (CoMP) for LTE-Advanced was put forward in April 2008, as a tool to improve the coverage of cells having high data rates, the cell-edge throughput and/or to increase system throughput. This book mainly focuses on the Group Cell architecture with multi-cell generalized coordination, Contrast Analysis between Group Cell architecture and CoMP, Capacity Analysis, Slide Handover Strategy, Power Allocation schemes of Group Cell architecture to mitigate the inter-cell interference and maximize system capacity and the trial network implementation and performance evaluations of Group Cell architecture.