Connected Dominating Set: Theory and Applications

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.

-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