This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON RELIABILITY 1 Design and Evaluation of Algorithms for Energy Efficient and Complete Determination of Critical Nodes for Wireless Sensor Network Reliability Orhan Dagdeviren , Member, IEEE, Vahid Khalilpour Akram, Member, IEEE, and Bulent Tavli , Senior Member, IEEE Abstract—A critical node (cut vertex or articulation point) in wireless sensor networks, is a node which its failure breaks the connectivity of the network. Therefore, it is crucial that critical nodes be detected and treated with caution. This paper provides two localized distributed algorithms for determining the states of nodes (critical or noncritical). The first proposed algorithm iden- tifies most of the critical and noncritical dominator nodes from two-hop local subgraph and connected dominating set (CDS) in- formation that limits the computational complexity to O(Δ 2 ) and bit complexity to O(clog 2 n) where Δ is the maximum node de- gree, c is the critical node count, and n is the node count. The testbed experiments and simulation results show that this algo- rithm detects up to 93% of critical nodes and achieves up to 91% of state determination with low energy consumption. The second proposed algorithm, which is based on the first one, finds the states of all nodes by running a limited distributed depth-first search algorithm in unrecognized parts of the network without travers- ing the whole network. Comprehensive testbed experiments and simulation results reveal that, in the presence of a CDS, this algo- rithm finds all critical nodes with lower energy consumption than all existing algorithms. Index Terms—Connected dominating set (CDS), connectivity, critical node, depth-first search (DFS), reliability, wireless sensor networks (WSNs). I. INTRODUCTION R ECENT advances in sensor devices and wireless communications have increased the usage of wireless sensor networks (WSNs) in many application areas and scenarios, including military operations, environment control, intelligent structures and tools, tracking systems, and industrial applications [1]–[4]. Typically, sensor nodes in a WSN are Manuscript received December 14, 2017; revised June 1, 2018 and Au- gust 31, 2018; accepted September 1, 2018. This work was supported by TUBITAK (Scientific and Technical Research Council of Turkey) under grant 113E470. This paper was presented in part at the IEEE SENSORS Confer- ence, Orlando, FL, USA, October 30–November 2, 2016. Associate Editor: P. Laplante. (Corresponding author: Orhan Dagdeviren.) O. Dagdeviren and V. K. Akram are with the International Computer Institute, Ege University, Izmir 35100, Turkey (e-mail:, orhan.dagdeviren@ege.edu.tr; vahid59@gmail.com). B. Tavli is with the Department of Electrical and Electronics Engineer- ing, TOBB University of Economics and Technology, Ankara 06510, Turkey (e-mail:, btavli@etu.edu.tr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TR.2018.2873917 Fig. 1. Network model. battery-powered autonomous devices that are distributed over a predetermined sensing environment to collect information. In a typical WSN deployment, data acquired by the sensor nodes are conveyed toward the sink node in a multihop fashion (i.e., sensor nodes act as relay nodes). One of the greatest advantages of WSNs is that they do not need a fixed infrastructure (i.e., sensor nodes create and main- tain network connectivity in ad hoc mode). However, due to the fact that each node establishes physical connectivity with other nodes in its direct communication range, failure of certain nodes has a potential to impact unproportionately high num- ber of other sensor nodes’ connectivity that in turn affects the network reliability [5]. Failures in some nodes may disconnect all paths between the sink and a plurality of sensor nodes. In the worst case, if a critical node (cut vertex) stops working, a large collection of nodes may be separated from the network. For example, in Fig. 1, a failure in node 2 disconnects nodes {3, 4, 5} from other nodes in the network. All black nodes in Fig. 1 are critical nodes. Critical nodes reduce the reliability of WSNs by increasing the disconnection probability in the network. Hence, determin- ing (and resolving) the critical nodes is one of the vital tasks for establishing a reliable WSN. Yet, determining the critical nodes has a potential to deplete the limited energy of WSN nodes and to become a costly operation. Instead of finding the critical nodes using a separate algorithm, we propose two algo- rithms that can determine the states of nodes using connected dominating set (CDS) that is a connected subset of nodes such that each node in the network either is in dominating set or has at least one neighbor in dominating set. CDS is a widely used 0018-9529 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.