Abstract-In two-tiered wireless sensor networks (WSNs), relay node placement is one of the key factors impacting the network energy consumption and the system overhead. In this paper, a novel connectivity-aware approximation algorithm for relay node placement in the WSNs is proposed to offer a major step forward in saving system overhead. In particular, a unique local search approximation algorithm (LSAA) is introduced to solve the relay node single cover (RNSC) problem. In this proposed LSAA approach, the sensor nodes are allocated into groups and then a local set cover (SC) for each group is achieved by a local search algorithm. The union set of all the local SCs constitutes a SC of the RNSC problem. The approximation ratio and the time complexity of the LSAA are analyzed by rigorous proof. In addition, the LSAA approach has been extended to solve the relay node double cover problem. Then, a relay location selection algorithm (RLSA) is proposed to utilize the resulting SC from the LSAA in combining RLSA with the minimum spanning tree heuristic to build the high-tier connectivity. As the RLSA searches for a nearest location to the sink node for each relay node, the high-tier network built by the RLSA becomes denser than that by existing works. As a result, the number of added relay nodes for building the connectivity of the high-tier WSN can be significantly saved. Simulation results clearly demonstrate that the proposed LSAA outperforms the approaches reported in literature and the RLSA-based algorithm can noticeably save relay nodes newly deployed for the high-tier connectivity.Index Terms-Wireless sensor networks, relay node placement, geometric disc cover, network connectivity, approximation algorithm.

No abstract

The Delay Constrained Relay Node Placement (DCRNP) problem in Wireless Sensor Networks (WSNs) aims to deploy minimum relay nodes such that for each sensor node there is a path connecting this sensor node to the sink without violating delay constraint. As WSNs are gradually employed in time-critical applications, the importance of the DCRNP problem becomes noticeable. For the NP-hard nature of DCRNP problem, an approximation algorithm-Set-Covering-based Relay Node Placement (SCA) is proposed to solve the DCRNP problem in this paper. The proposed SCA algorithm deploys relay nodes iteratively from sink to the given sensor nodes in hops, i.e., in the kth iteration SCA deploys relay nodes at the locations that are k hops apart from the sink. Specifically, in each iteration, SCA first finds the candidate deployment locations located within 1 hop to the relay nodes and sensor nodes, which have already been connected to the sink. Then, a subset of these candidate deployment locations, which can guarantee the existence of paths connecting unconnected sensor nodes to the sink within delay constraint, is selected to deploy relay nodes based on the set covering method. As the iteration of SCA algorithm, the sensor nodes are gradually connected to the sink with satisfying delay constraint.The elaborated analysis of the approximation ratio of SCA algorithm is given out, and we also prove that the SCA is a polynomial time algorithm through rigorous time complexity analysis. To evaluate the performance of the proposed SCA algorithm, extensive simulations are implemented, and the simulation results show that the SCA algorithm can significantly save the deployed relay nodes comparing to the existing algorithms, i.e., at most 31.48% deployed relay nodes can be saved due to SCA algorithm.Index Terms-Wireless sensor networks, set covering, delay constrained relay node placement, approximation algorithm.• An approach is designed to represent each CDL or SN by the unconnected SNs, which can be connected to the sink