Coverage and connectivity in wireless networks

The limited energy resources, instability, and lacking central control in wireless networks motivates the study of connected dominating set (CDS) which serves as routing backbone to support service discovery, and area monitoring and also broadcasting. The construction of CDS involves both coverage and connectivity. We first study several problems related to coverage. Given are a set of nodes and targets in a plane, the problem Minimum Wireless Cover (MWC) seeks the fewest nodes to cover the targets. If all nodes are associated with some positive prices, the problem Cheapest Wireless Cover (CWC) seeks a cheapest set of nodes to cover the targets. If all nodes have bounded lives, the problem Max-Life Wireless Cover (MLWC) seeks a wireless coverage schedule of maximum life subject to the life constraints of individual nodes. We present a polynomial time approximation scheme (PTAS) for MWC, and two randomized approximation algorithms for CWC and MLWC respectively. We also propose a (4+e)-approximation algorithm for the problem Minimum-Weighted Dominating Set in unit disk graphs. Meanwhile, for the connecting part, given a node-weighted connected graph and a subset of terminals, the problem Node-Weighted Steiner Tree (NWST) seeks a lightest tree connecting a given set of terminals in a node-weighted graph. We present three approximation algorithms for NWST restricted to UDGs. This dissertation also explores the applications of CDS, and develops efficient algorithms for the applications such as real-time aggregation scheduling in wireless networks. Given a set of periodic aggregation queries, each query has its own period, and the subset of source nodes containing the data, we first propose a family of efficient and effective real-time scheduling protocols that can answer every job of each query task within a relative delay under resource constraints by addressing the following tightly coupled tasks: routing, transmission plan constructions, node activity scheduling, and packet scheduling. Based on our protocol design, we further propose schedulability test schemes to efficiently and effectively test whether, for a set of queries, each query job can be finished within a finite delay.