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

Heavy-tailed Distributions In Stochastic Dynamical Models

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics

Minimum-Cost Coverage of Point Sets by Disks

We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t_j) and radii (r_j) that cover a given set of demand points Y in the plane at the smallest possible cost. We consider cost functions of the form sum_j f(r_j), where f(r)=r^alpha is the cost of transmission to radius r. Special cases arise for alpha=1 (sum of radii) and alpha=2 (total area); power consumption models in wireless network design often use an exponent alpha>2. Different scenarios arise according to possible restrictions on the transmission centers t_j, which may be constrained to belong to a given discrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t_j on a given line in order to cover demand points Y in the plane; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set of transmission points in the plane and any fixed alpha>1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks.Comment: 10 pages, 4 figures, Latex, to appear in ACM Symposium on Computational Geometry 200