This book reviews problems in connected dominating set theory, discussing motivation and overview, problem complexity analysis and approximation algorithm designs. Readers will clearly grasp background, formulation, major research results and open problems.

The connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, especially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. In this book, we are going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets. The book consists of 16 chapters. Except the 1st one, each chapter is devoted to one problem, and consists of three parts, motivation and overview, problem complexity analysis, and approximation algorithm designs, which will lead the reader to see clearly about the background, formulation, existing important research results, and open problems. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics.

This unique book may be used as a reference and/or supplementary text in a graduate seminar The expository content and complete list of references in each chapter bring the reader quickly to the forefront of research Wide applications of connected dominating sets attract readers not only from optimization and theoretical computer science, but also from computer communication networks and industrial engineering

Autorentext

Ding-Zhu Du is Professor of Computer Science at the University of Texas at Dallas. For a number of years he was the Editor-in-Chief of the Journal of Combinatorial Optimization and the combinatorial optimization series editor for the SOIA book series. Professor Du is co-editor of the first and second editions of the Handbook of Combinatorial Optimization. He was also co-author (with Pardalos and Wu) of the Kluwer publication "Mathematical Theory of Optimization." Panos M. Pardalos is Distinguished Professor Emeritus of Industrial and Systems Engineering at the University of Florida. Additionally, he is the Paul and Heidi Brown Preeminent Professor in Industrial & Systems Engineering. He is also an affiliated faculty member of the Computer and Information Science Department, the Hellenic Studies Center, and the Biomedical Engineering Program. He is also the Director of the Center for Applied Optimization. Dr. Pardalos is a world leading expert in global and combinatorial optimization. His recent research interests include network design problems, optimization in telecommunications, e-commerce, data mining, biomedical applications, and massive computing. He has co-authored and co-edited more than 30 books, as well as publishing more than 600 journal articles and conference proceedings. Prof. Pardalos is a Fellow of AAAS (American Association for the Advancement of Science), Fellow of American Institute for Medical and Biological Engineering (AIMBE), and EUROPT. He is a Distinguished International Professor by the Chinese Minister of Education; Honorary Professor of Anhui University of Sciences and Technology, China; Elizabeth Wood Dunlevie Honors Term Professor; Honorary Doctor, V.M. Glushkov Institute of Cybernetics of The National Academy of Sciences of Ukraine; Foreign Associate Member of Reial Academia de Doctors, Spain; and Advisory board member of the Centre for Optimisation and Its Applications, Cardiff University, UK. He is also the recipient of UF 2009 International Educator Award; Medal (in recognition of broad contributions in science and engineering) of the University of Catani, Italy; EURO Gold Medal (EGM); Honorary Doctor of Science Degree, Wilfrid Laurier University, Canada; Senior Fulbright Specialist Award; University of Florida Research Foundation Professorship; and IBM Achievement Award. Xiaodong Hu is a research professor at the Institute of Applied Mathematics, Chinese Academy of Sciences. He was the president of OR society of China a few year ago. His research interests include combinatorial optimization, and approximation algorithms, to name just two. Weili Wu is pra ofessor of computer science at the University of Texas at Dallas. Her research interests include optimization theory, big data management and analysis, social networks, database systems, and wireless sensor networks, to name just several. She has published more than200 journal papers and 100 conference papers. Especially, she made several influential contributions in the study of wireless sensor networks, which are accumulated in a Springer publication "Optimal Coverage in Wireless Sensor Networks".

Klappentext

The connected dominating set (CDS) has been a classic subject studied in graph theory since 1975. It has been discovered in recent years that CDS has important applications in communication networks especially in wireless networks as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. This work is a valuable reference for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, industrial engineering, and discrete mathematics. The book may also be used as a text in a graduate seminar for PhD students. Readers should have a basic knowledge of computational complexity and combinatorial optimization.

In this book, the authors present the state-of-the-art in the study of connected dominating sets. Each chapter is devoted to one problem, and consists of three parts: motivation and overview, problem complexity analysis, and approximation algorithm designs. The text is designed to give the reader a clear understanding of the background, formulation, existing important research results, and open problems. Topics include minimum CDS, routing-cost constrained CDS, weighted CDS, directed CDS, SCDS (strongly connected dominating set), WCDS (weakly connected dominating set), CDS-partition, virtual backbone in wireless networks, convertor placement in optical networks, coverage in wireless sensor networks, and more.

Inhalt
-Preface.-1. Introduction.-2. CDS in General Graph-3. CDS in Unit Disk Graph.-4. CDS in Unit Ball Graphs and Growth Bounded Graphs.-5. Weighted CDS in Unit Disk Graph.-6. Coverage.-7. Routing-Cost Constrained CDS.-8. CDS in Disk-Containment Graphs.-9. CDS in Disk-Intersection Graphs.-10. Geometric Hitting Set and Disk Cover.-11. Minimum-Latency Scheduling.-12 CDS in Planar Graphs.-Bibliography