Natural Science Foundation of China under Grant 61304263, 61673371 and 71602124, and Liaoning Provincial Natural Science Foundation of China under Grant 2014020081.
Delay constrained relay node placement (DCRNP) problem minimizes the quantity of deployed relays that are employed to build at least one path between the sink and each sensor, while guaranteeing that the delay constraints for the built paths are fulfilled. Published literature only focus on the DCRNP problem in single-tiered wireless sensor networks (WSNs). Considering the benefits in terms of network scalability and energy consumption by the two-tiered network topology, this paper studies the DCRNP problem in two-tiered WSNs and proposes a pruning-and-substitution-based-heuristic (PSH) algorithm to solve the DCRNP problem. PSH consists of two phases, i.e., the covering phase and the connecting phase. In the covering phase, a shortest-path-based algorithm (SPA) is proposed to deploy relays at a subset of predetermined deployment locations such that each sensor is covered by at least one relay, meanwhile ensuring the obedience of delay constraints. Then, in the connecting phase, a tree-based connecting algorithm (TCA) is proposed to build the high-tier network connectivity. TCA first builds a shortest path tree to connect the relays deployed by SPA to the sink, and then, saves the deployed relays by gradually pruning or substituting them by the relays placed at the locations that several feasible paths pass through. The time complexity and the approximation ratio of this work are explicitly analyzed and extensive simulations are implemented to demonstrate its effectiveness.