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The Fascinating World of Graph Theory

by Arthur Benjamin Ping Zhang Gary Chartrand

The fascinating world of graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory's development and the vibrant individuals responsible for the field's growth.Introducing graph theory's fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight's Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor.An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.

Group Cell Architecture for Cooperative Communications

by Ping Zhang Qimei Cui Xiaodong Xu Xiaofeng Tao

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.

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