Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

A 10-Approximation of the ?/2-MST

Bounded-angle spanning trees of points in the plane have received considerable attention in the context of wireless networks with directional antennas. For a point set P in the plane and an angle ?, an ?-spanning tree (?-ST) is a spanning tree of the complete Euclidean graph on P with the property that all edges incident to each point p ? P lie in a wedge of angle ? centered at p. The ?-minimum spanning tree (?-MST) problem asks for an ?-ST of minimum total edge length. The seminal work of Anscher and Katz (ICALP 2014) shows the NP-hardness of the ?-MST problem for ? = 2?/3, ? and presents approximation algorithms for ? = ?/2, 2?/3, ?. In this paper we study the ?-MST problem for ? = ?/2 which is also known to be NP-hard. We present a 10-approximation algorithm for this problem. This improves the previous best known approximation ratio of 16

Bounded-Angle Minimum Spanning Trees

Motivated by the connectivity problem in wireless networks with directional antennas, we study bounded-angle spanning trees. Let P be a set of points in the plane and let ? be an angle. An ?-ST of P is a spanning tree of the complete Euclidean graph on P with the property that all edges incident to each point p ? P lie in a wedge of angle ? centered at p. We study the following closely related problems for ? = 120 degrees (however, our approximation ratios hold for any ? ? 120 degrees). 1) The ?-minimum spanning tree problem asks for an ?-ST of minimum sum of edge lengths. Among many interesting results, Aschner and Katz (ICALP 2014) proved the NP-hardness of this problem and presented a 6-approximation algorithm. Their algorithm finds an ?-ST of length at most 6 times the length of the minimum spanning tree (MST). By adopting a somewhat similar approach and using different proof techniques we improve this ratio to 16/3. 2) To examine what is possible with non-uniform wedge angles, we define an ??-ST to be a spanning tree with the property that incident edges to all points lie in wedges of average angle ?. We present an algorithm to find an ??-ST whose largest edge-length and sum of edge lengths are at most 2 and 1.5 times (respectively) those of the MST. These ratios are better than any achievable when all wedges have angle ?. Our algorithm runs in linear time after computing the MST

Wireless Sensor Localization: Error Modeling and Analysis for Evaluation and Precision

Wireless sensor networks (WSNs) have shown promise in a broad range of applications. One of the primary challenges in leveraging WSNs lies in gathering accurate position information for the deployed sensors while minimizing power cost. In this research, detailed background research is discussed regarding existing methods and assumptions of modeling methods and processes for estimating sensor positions. Several novel localization methods are developed by applying rigorous mathematical and statistical principles, which exploit constraining properties of the physical problem in order to produce improved location estimates. These methods are suitable for one-, two-, and three-dimensional position estimation in ascending order of difficulty and complexity. Unlike many previously existing methods, the techniques presented in this dissertation utilize practical, realistic assumptions and are progressively designed to mitigate incrementally discovered limitations. The design and results of a developed multiple-layered simulation environment are also presented that model and characterize the developed methods. The approach, developed methodologies, and software infrastructure presented in this dissertation provide a framework for future endeavors within the field of wireless sensor networks

Ice-creams and wedge graphs

Abstract What is the minimum angle α > 0 such that given any set of α-directional antennas (that is, antennas each of which can communicate along a wedge of angle α), one can always assign a direction to each antenna such that the resulting communication graph is connected? Here two antennas are connected by an edge if and only if each lies in the wedge assigned to the other. This problem was recently presented by Carmi, Katz, Lotker, and Rosén [2] who also found the minimum such α namely α = π 3 . In this paper we give a simple proof of this result. Moreover, we obtain a much stronger and optimal result (see Theorem 1) saying in particular that one can chose the directions of the antennas so that the communication graph has diameter ≤ 4. Our main tool is a surprisingly basic geometric lemma that is of independent interest. We show that for every compact convex set S in the plane and every 0 < α < π, there exist a point O and two supporting lines to S passing through O and touching S at two single points X and Y , respectively, such that |OX| = |OY | and the angle between the two lines is α

Robust, Resilient Networked Communication in Challenged Environments

In challenged environments, digital communication infrastructure may be difficult or even impossible to access. This is especially true in rural and developing regions, as well as in any region during a time of political or environmental crisis. We advance the state of the art in wireless networking and security to design networks and applications that rapidly assess changing networking conditions to restore communication and provide local situational awareness. This dissertation examines new systems for responding to current and emerging needs for wireless networks. This work looks across the wireless ecosystem of widely deployed standards. We develop new tools to improve network assessment and to provide robust and reliable network communication. By incorporating new technological breakthroughs, such as the wide commercial success of Unmanned Aircraft Systems (UAS), we introduce novel methods and systems for existing wireless standards for these challenged networks. We assess how existing technologies and standards function in difficult environments: lacking end-end Internet connectivity, experiencing overload or other resource constraints, and operating in three dimensional space. Through this lens, we demonstrate how to optimize networks to serve marginalized communities outside of first world urban cities and make our networks resilient to natural and political crisis that threaten communication

Finite-Time Distributed Algorithms for Verifying and Ensuring Strong Connectivity of Directed Networks

The strong connectivity of a directed graph associated with the communication network topology is crucial in ensuring the convergence of many distributed estimation/control/optimization algorithms. However, the assumption on the network's strong connectivity may not always be satisfied in practice. In addition, information on the overall network topology is often not available, e.g., due to privacy concerns or geographical constraints which calls for a distributed algorithm. This paper aims to fill a crucial gap in the literature due to the absence of a fully distributed algorithm to verify and ensure in finite-time the strong connectivity of a directed network. Specifically, inspired by the maximum consensus algorithm we propose distributed algorithms that enable individual node in a networked system to verify the strong connectivity of a directed graph and further, if necessary, augment a minimum number of new links to ensure the directed graph's strong connectivity. The proposed distributed algorithms are implemented without requiring information of the overall network topology and are scalable as they only require finite storage and converge in finite number of steps. Furthermore, the algorithms also preserve the privacy in terms of the overall network's topology. Finally, the proposed distributed algorithms are demonstrated and evaluated via numerical results.acceptedVersionPeer reviewe

Fault-tolerant Stochastic Distributed Systems

The present doctoral thesis discusses the design of fault-tolerant distributed systems, placing emphasis in addressing the case where the actions of the nodes or their interactions are stochastic. The main objective is to detect and identify faults to improve the resilience of distributed systems to crash-type faults, as well as detecting the presence of malicious nodes in pursuit of exploiting the network. The proposed analysis considers malicious agents and computational solutions to detect faults. Crash-type faults, where the affected component ceases to perform its task, are tackled in this thesis by introducing stochastic decisions in deterministic distributed algorithms. Prime importance is placed on providing guarantees and rates of convergence for the steady-state solution. The scenarios of a social network (state-dependent example) and consensus (time- dependent example) are addressed, proving convergence. The proposed algorithms are capable of dealing with packet drops, delays, medium access competition, and, in particular, nodes failing and/or losing network connectivity. The concept of Set-Valued Observers (SVOs) is used as a tool to detect faults in a worst-case scenario, i.e., when a malicious agent can select the most unfavorable sequence of communi- cations and inject a signal of arbitrary magnitude. For other types of faults, it is introduced the concept of Stochastic Set-Valued Observers (SSVOs) which produce a confidence set where the state is known to belong with at least a pre-specified probability. It is shown how, for an algorithm of consensus, it is possible to exploit the structure of the problem to reduce the computational complexity of the solution. The main result allows discarding interactions in the model that do not contribute to the produced estimates. The main drawback of using classical SVOs for fault detection is their computational burden. By resorting to a left-coprime factorization for Linear Parameter-Varying (LPV) systems, it is shown how to reduce the computational complexity. By appropriately selecting the factorization, it is possible to consider detectable systems (i.e., unobservable systems where the unobservable component is stable). Such a result plays a key role in the domain of Cyber-Physical Systems (CPSs). These techniques are complemented with Event- and Self-triggered sampling strategies that enable fewer sensor updates. Moreover, the same triggering mechanisms can be used to make decisions of when to run the SVO routine or resort to over-approximations that temporarily compromise accuracy to gain in performance but maintaining the convergence characteristics of the set-valued estimates. A less stringent requirement for network resources that is vital to guarantee the applicability of SVO-based fault detection in the domain of Networked Control Systems (NCSs)