On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

Energy efficient clustering and secure data aggregation in wireless sensor networks

Communication consumes the majority of a wireless sensor network\u27s limited energy. There are several ways to reduce the communication cost. Two approaches used in this work are clustering and in-network aggregation. The choice of a cluster head within each cluster is important because cluster heads use additional energy for their responsibilities and that burden needs to be carefully distributed. We introduce the energy constrained minimum dominating set (ECDS) to model the problem of optimally choosing cluster heads in the presence of energy constraints. We show its applicability to sensor networks and give an approximation algorithm of O(log n) for solving the ECDS problem. We propose a distributed algorithm for the constrained dominating set which runs in O(log n log [triangle]) rounds with high probability. We show experimentally that the distributed algorithm performs well in terms of energy usage, node lifetime, and clustering time and thus is very suitable for wireless sensor networks. Using aggregation in wireless sensor networks is another way to reduce the overall communication cost. However, changes in security are necessary when in- network aggregation is applied. Traditional end-to-end security is not suitable for use with in-network aggregation. A corrupted sensor has access to the intermediate data and can falsify results. Additively homomorphic encryption allows for aggregation of encrypted values, with the result being the same as the result as if unencrypted data were aggregated. Using public key cryptography, digital signatures can be used to achieve integrity. We propose a new algorithm using homomorphic encryption and additive digital signatures to achieve confidentiality, integrity and availability for in- network aggregation in wireless sensor networks. We prove that our digital signature algorithm which is based on Elliptic Curve Digital Signature Algorithm (ECDSA) is at least as secure as ECDSA. Even without in-network aggregation, security is a challenge in wireless sensor networks. In wireless sensor networks, not all messages need to be secured with the same level of encryption. We propose a new algorithm which provides adequate levels of security while providing much higher availablility [sic] than other security protocols. Our approach uses similar amounts of energy as a network without security --Abstract, page iv

Review of Optimization Problems in Wireless Sensor Networks

International audienc

Connectivity, Coverage and Placement in Wireless Sensor Networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes

Connected Dominating Set Based Topology Control in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are now widely used for monitoring and controlling of systems where human intervention is not desirable or possible. Connected Dominating Sets (CDSs) based topology control in WSNs is one kind of hierarchical method to ensure sufficient coverage while reducing redundant connections in a relatively crowded network. Moreover, Minimum-sized Connected Dominating Set (MCDS) has become a well-known approach for constructing a Virtual Backbone (VB) to alleviate the broadcasting storm for efficient routing in WSNs extensively. However, no work considers the load-balance factor of CDSsin WSNs. In this dissertation, we first propose a new concept — the Load-Balanced CDS (LBCDS) and a new problem — the Load-Balanced Allocate Dominatee (LBAD) problem. Consequently, we propose a two-phase method to solve LBCDS and LBAD one by one and a one-phase Genetic Algorithm (GA) to solve the problems simultaneously. Secondly, since there is no performance ratio analysis in previously mentioned work, three problems are investigated and analyzed later. To be specific, the MinMax Degree Maximal Independent Set (MDMIS) problem, the Load-Balanced Virtual Backbone (LBVB) problem, and the MinMax Valid-Degree non Backbone node Allocation (MVBA) problem. Approximation algorithms and comprehensive theoretical analysis of the approximation factors are presented in the dissertation. On the other hand, in the current related literature, networks are deterministic where two nodes are assumed either connected or disconnected. In most real applications, however, there are many intermittently connected wireless links called lossy links, which only provide probabilistic connectivity. For WSNs with lossy links, we propose a Stochastic Network Model (SNM). Under this model, we measure the quality of CDSs using CDS reliability. In this dissertation, we construct an MCDS while its reliability is above a preset applicationspecified threshold, called Reliable MCDS (RMCDS). We propose a novel Genetic Algorithm (GA) with immigrant schemes called RMCDS-GA to solve the RMCDS problem. Finally, we apply the constructed LBCDS to a practical application under the realistic SNM model, namely data aggregation. To be specific, a new problem, Load-Balanced Data Aggregation Tree (LBDAT), is introduced finally. Our simulation results show that the proposed algorithms outperform the existing state-of-the-art approaches significantly