Robust Component-based Network Localization with Noisy Range Measurements

Accurate and robust localization is crucial for wireless ad-hoc and sensor networks. Among the localization techniques, component-based methods advance themselves for conquering network sparseness and anchor sparseness. But component-based methods are sensitive to ranging noises, which may cause a huge accumulated error either in component realization or merging process. This paper presents three results for robust component-based localization under ranging noises. (1) For a rigid graph component, a novel method is proposed to evaluate the graph's possible number of flip ambiguities under noises. In particular, graph's \emph{MInimal sepaRators that are neaRly cOllineaR (MIRROR)} is presented as the cause of flip ambiguity, and the number of MIRRORs indicates the possible number of flip ambiguities under noise. (2) Then the sensitivity of a graph's local deforming regarding ranging noises is investigated by perturbation analysis. A novel Ranging Sensitivity Matrix (RSM) is proposed to estimate the node location perturbations due to ranging noises. (3) By evaluating component robustness via the flipping and the local deforming risks, a Robust Component Generation and Realization (RCGR) algorithm is developed, which generates components based on the robustness metrics. RCGR was evaluated by simulations, which showed much better noise resistance and locating accuracy improvements than state-of-the-art of component-based localization algorithms.Comment: 9 pages, 15 figures, ICCCN 2018, Hangzhou, Chin

Minimum Sparsity of Unobservable Power Network Attacks

Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $\kappa(G^M) + 1$, where $\kappa(G^M)$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact as functions of the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.Comment: submitted to IEEE Transactions on Automatic Contro

Energy Complexity of Distance Computation in Multi-hop Networks

Energy efficiency is a critical issue for wireless devices operated under stringent power constraint (e.g., battery). Following prior works, we measure the energy cost of a device by its transceiver usage, and define the energy complexity of an algorithm as the maximum number of time slots a device transmits or listens, over all devices. In a recent paper of Chang et al. (PODC 2018), it was shown that broadcasting in a multi-hop network of unknown topology can be done in $\text{poly} \log n$ energy. In this paper, we continue this line of research, and investigate the energy complexity of other fundamental graph problems in multi-hop networks. Our results are summarized as follows. 1. To avoid spending $\Omega(D)$ energy, the broadcasting protocols of Chang et al. (PODC 2018) do not send the message along a BFS tree, and it is open whether BFS could be computed in $o(D)$ energy, for sufficiently large $D$. In this paper we devise an algorithm that attains $\tilde{O}(\sqrt{n})$ energy cost. 2. We show that the framework of the ${\Omega}(n)$ round lower bound proof for computing diameter in CONGEST of Abboud et al. (DISC 2017) can be adapted to give an $\tilde{\Omega}(n)$ energy lower bound in the wireless network model (with no message size constraint), and this lower bound applies to $O(\log n)$-arboricity graphs. From the upper bound side, we show that the energy complexity of $\tilde{O}(\sqrt{n})$ can be attained for bounded-genus graphs (which includes planar graphs). 3. Our upper bounds for computing diameter can be extended to other graph problems. We show that exact global minimum cut or approximate $s$--$t$ minimum cut can be computed in $\tilde{O}(\sqrt{n})$ energy for bounded-genus graphs

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems