Complexity of increasing the secure connectivity in wireless ad hoc networks

We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the post-deployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing a secret key using only the links that are already secured by shared keys. This problem is in NP-hard and does not accept polynomial time approximation scheme PTAS since minimum cutsets to be augmented do not admit constant costs. The second one extends the first problem by increasing the power level between a pair of nodes that has a secret key to enable them physically connect. This problem can be formulated as the optimal key establishment problem with interference constraints with bi-objectives: (i) maximizing the concurrent key establishment flow, (ii) minimizing the cost. We prove that both problems are NP-hard and MAX-SNP with a reduction to MAX3SAT problem

A Novel Approach to Transmission Power, Lifetime and Connectivity Optimization in Asymmetric Networks

This thesis deals with the problem of proper power management over asymmetric networks represented by weighted directed graphs (digraphs) in the presence of various constraints. Three different problems are investigated in this study. First, the problem of total transmission power optimization and connectivity control over the network is examined. The notion of generalized algebraic connectivity (GAC), used as a network connectivity measure, is formulated as an implicit function of the nodes' transmission powers. An optimization problem is then presented to minimize the total transmission power of the network while considering constraints on the values of the GAC and the individual transmission power levels. The problem of network lifetime maximization and connectivity control is investigated afterwards. Each node is assumed to deplete its battery linearly with respect to the transmission powers used for communication, and the network lifetime is defined as the minimum lifetime over all nodes. Finally, it is desired to maximize the connectivity level of the network with constraints on the total transmission power of the network and the individual transmission powers. The interior point and the mixed interior point-exterior point methods are utilized to transform these constrained optimization problems into sequential optimization problems. Given the new formulation, each subproblem is then solved numerically via the subgradient method with backtracking line search. A distributed version of the algorithm, taking into account the estimation of global quantities, is provided. The asymptotic convergence of the proposed centralized and distributed algorithms is demonstrated analytically, and their effectiveness is verified by simulations

Interference-Aware Scheduling for Connectivity in MIMO Ad Hoc Multicast Networks

We consider a multicast scenario involving an ad hoc network of co-channel MIMO nodes in which a source node attempts to share a streaming message with all nodes in the network via some pre-defined multi-hop routing tree. The message is assumed to be broken down into packets, and the transmission is conducted over multiple frames. Each frame is divided into time slots, and each link in the routing tree is assigned one time slot in which to transmit its current packet. We present an algorithm for determining the number of time slots and the scheduling of the links in these time slots in order to optimize the connectivity of the network, which we define to be the probability that all links can achieve the required throughput. In addition to time multiplexing, the MIMO nodes also employ beamforming to manage interference when links are simultaneously active, and the beamformers are designed with the maximum connectivity metric in mind. The effects of outdated channel state information (CSI) are taken into account in both the scheduling and the beamforming designs. We also derive bounds on the network connectivity and sum transmit power in order to illustrate the impact of interference on network performance. Our simulation results demonstrate that the choice of the number of time slots is critical in optimizing network performance, and illustrate the significant advantage provided by multiple antennas in improving network connectivity.Comment: 34 pages, 12 figures, accepted by IEEE Transactions on Vehicular Technology, Dec. 201

Research on Wireless Multi-hop Networks: Current State and Challenges

Wireless multi-hop networks, in various forms and under various names, are being increasingly used in military and civilian applications. Studying connectivity and capacity of these networks is an important problem. The scaling behavior of connectivity and capacity when the network becomes sufficiently large is of particular interest. In this position paper, we briefly overview recent development and discuss research challenges and opportunities in the area, with a focus on the network connectivity.Comment: invited position paper to International Conference on Computing, Networking and Communications, Hawaii, USA, 201

Coverage Protocols for Wireless Sensor Networks: Review and Future Directions

The coverage problem in wireless sensor networks (WSNs) can be generally defined as a measure of how effectively a network field is monitored by its sensor nodes. This problem has attracted a lot of interest over the years and as a result, many coverage protocols were proposed. In this survey, we first propose a taxonomy for classifying coverage protocols in WSNs. Then, we classify the coverage protocols into three categories (i.e. coverage aware deployment protocols, sleep scheduling protocols for flat networks, and cluster-based sleep scheduling protocols) based on the network stage where the coverage is optimized. For each category, relevant protocols are thoroughly reviewed and classified based on the adopted coverage techniques. Finally, we discuss open issues (and recommend future directions to resolve them) associated with the design of realistic coverage protocols. Issues such as realistic sensing models, realistic energy consumption models, realistic connectivity models and sensor localization are covered

Consensus, Cohesion and Connectivity

Social life clusters into groups held together by ties that also transmit information. When collective problems occur, group members use their ties to discuss what to do and to establish an agreement, to be reached quick enough to prevent discounting the value of the group decision. The speed at which a group reaches consensus can be predicted by the algebraic connectivity of the network, which also imposes a lower bound on the group's cohesion. This specific measure of connectivity is put to the test by re-using experimental data, which confirm the prediction