Wireless sensor networks are gradually employed in many applications that require reliable and real-time data transmission. As hop count is an important factor affecting end-toend delay and reliability, we investigate the hop constrained relay node placement (HCRNP) problem in this paper. First, to achieve connectivity requirement, we study the connected HCRNP problem. Then, to design survivable network topologies against node failures, we study the 2-connected HCRNP problem. Correspondingly, two polynomial-time algorithms: cover-based 1-connected node placement (C1NP) and cover-based 2-connected node placement (C2NP) are proposed, respectively, to address the above two problems. Through rigorous analysis, we show that 1) C1NP has an approximation ratio better than existing algorithms for the connected HCRNP problem (i.e., O(1) for special settings and O(ln n) for arbitrary settings, where n is the number of SNs) and 2) C2NP is the first algorithm that can provide an explicit performance guarantee for the 2-connected HCRNP problem, i.e., whenever C2NP finds a feasible solution, the ratio of this solution to the optimal solution is guaranteed to be O(ln n). Finally, we verify the effectiveness of the proposed algorithms through extensive simulations. Index Terms-Approximation algorithm, quality of service, relay node placement (RNP), set cover, wireless sensor networks (WSNs). I. INTRODUCTION W IRELESS sensor networks (WSNs) have been employed in various applications, such as battlefield surveillance, environmental monitoring, industrial automation, and scientific observation. Typically, WSNs are composed of spatially distributed sensor nodes (SNs) gathering certain information and at least one sink collecting the information from SNs. Normally, an SN has a very limited communication range mainly due to its constrained power supply and antenna height [1]-[4]. As a result, some additional nodes are placed to build the network connectivity, and these nodes function as relay nodes Manuscript