A Simple Algorithm for Fault-Tolerant Topology Control in Wireless Sensor Network Jianhui Zhang ∗ , Jiming Chen ∗ , Yu Wang † , Yang Xiao ‡ and Youxian Sun ∗ ∗ State Key Lab of Industrial Control Technology, Zhejiang University, P.R.China Email: {jhzhang,yxsun}@iipc.zju.edu.cn; jmchen@ieee.org † Department of Computer Science, University of North Carolina at Charlotte, USA Email: wangyu@ieee.org ‡ Department of Computer Science, The University of Alabama, USA Email: yangxiao@ieee.org Abstract—To preserve network connectivity is an important issue especially in wireless sensor network, where wireless links are easy to be disturbed and tiny sensors are even easy to fail accidently. Therefore, it is necessary to design a fault-tolerant network. A feasible method is to construct a k-vertex connected topology. In this paper, we consider k-connectivity of wireless network and propose a simple global algorithm (GAFT k ) which preserves the network k-connectivity and reduces the maximal transmission power (TP). The average degree expectation of the topology generated by GAFT k is O “ (k+3) 2 4 ” . Based on GAFT k , we propose a simple local algorithm (LAFT k ) which preserves k-vertex connectivity while maintaining bi-directionality of the network. Simulation results show that GAFT/LAFT have better performance than other current fault-tolerant protocols. I. I NTRODUCTION Fault tolerant topology control (TC) is important in wireless networks, especially in wireless sensor network (WSN), since sensor nodes and wireless links are easy to fail and power and computational resource is limited. Many topology control algorithms have been designed to maintain network connectiv- ity while reducing energy consumption and improving network capacity [1]. A few of them have considered the fault-tolerance [2], [3], like CBTC k (α) [4]. The CBTC k (α) is an extension of CBTC from [5] to provide fault tolerant topology. In CBTC(α), every vertex increases its transmission power (TP) until either the maximum angle between its two consecutive neighbors is at most α (a constant depended on k) or its maximal power is reached. Therefore, the TP would adjust to a excessive value. Fault tolerant Local Spanning Sub-graph (FLSS k ) can pre- serve k-connectivity while maintaining bi-directionality [6]. It is based on a min-max optimal centralized algorithm, Fault tol- erant Global Spanning Sub-graph (FGSS k ). Whether FGSS k is k-connected that need be tested by using network flow This work is supported by the Nature Science Foundation of China under Grant 60604029, 60702081, Nature Science Foundation of Zhejiang Province under Grant Y106384,Y107309, Joint Funds of NSFC-Guangdong under Grant U0735003, the SRFDP under Grant 20050335020, the R&D Program of Zhejiang Province under Grant No.2007C31038 and 111 Projects under Grant B07031; The work of Yu Wang was supported in part by the National Science Foundation under Grant NeTS-NOSS-0721666 and by funds provided by the University of North Carolina at Charlotte;Prof. Xiao’s work was partially supported by the National Science Foundation under the grant CNS-0716211. techniques (NFT) [7], which results in much high complexity and cost of the algorithm. Furthermore redundant edges would be added to the topology when FLSS k locally constructs a subgraph. There have been several research efforts recently on the- oretically studying the necessary condition for k-connected topology [8] [9] and devising approximation algorithms to construct such topologies [4]. All of above fault-tolerant topology control algorithms either use unrealistic assumptions (i.e. the locations of all nodes and the exact distance among them are known) or involve complex calculation. In this paper, we proposal two TC algorithms with sim- ple calculation to preserve the network k-connectivity. The main contributions of this paper include: (a) the topologies constructed under GAFT k and LAFT k preserve the network k-connectivity; (b) the time complexity of both GAFT k and LAFT k is low, so that nodes with limited computational and power capacity can still afford these algorithms efficiently; (c) the resulting topology can be converted into one with only bidirectional links. The rest of the paper is organized as follows. Section II introduces our models and assumptions. Section III presents GAFT and its performance analysis, while Section IV gives its distributed implementation LAFT. Simulation study on both GAFT and LAFT is provided in Section V. Section VI concludes the paper. II. MODELS AND ASSUMPTIONS Assume that the nodes in network are uniformly deployed in a c × c area. Each node has an omni-directional antenna, which can adjust its TP discretely. Its transmission radius is denoted as r and its maximal value is denoted as r max . An undirected simple graph G =(V,E) is applied to analyze our TC algorithm, where V is the set of all nodes in the network and E is the edge set. |V | = n and |*| is the size of the set *. d(N u ,N v ) denotes the received signal strength indication difference (RD) between nodes N u and N v . So GAFT/LAFT do not depend on any radio propagation model. A unique address ID is assigned to each node. The one-hop neighborhood of a node N u , denoted as H 1 Nu , is the set of