David Kiyoshi Goldenberg

A Theory of Network Localization

In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly

Towards mobility as a network control primitive

In the near future, the advent of large-scale networks of mobile agents autonomously performing long-term sensing and communication tasks will be upon us. However, using controlled node mobility to improve communication performance is a capability that the mobile networking community has not yet investigated. In this paper, we study mobility as a network control primitive. More specifically, we present the first mobility control scheme for improving communication performance in such networks. Our scheme is completely distributed, requiring each node to possess only local information. Our scheme is self-adaptive, being able to transparently encompass several modes of operation, each respectively improving power efficiency for one unicast flow, multiple unicast flows, and many-to-one concast flows. We provide extensive evaluations on the feasibility of mobility control, showing that controlled mobility can improve network performance in many scenarios. This work constitutes a novel application of distributed control to networking in which underlying network communication serves as input to local control rules that guide the system toward a global objective.

Optimizing cost and performance for multihoming

Multihoming is often used by large enterprises and stub ISPs to connect to the Internet. In this paper, we design a series of novel smart routing algorithms to optimize cost and performance for multihomed users. We evaluate our algorithms through both analysis and extensive simulations based on realistic charging models, traffic demands, performance data, and network topologies. Our results suggest that these algorithms are very effective in minimizing cost and at the same time improving performance. We further examine the equilibrium performance of smart routing in a global setting and show that a smart routing user can improve its performance without adversely affecting other users.

Localization in sparse networks using sweeps

Determining node positions is essential for many next-generation network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for fine-grained localization called Sweeps. Sweeps correctly finitely localizes all nodes in bilateration networks. Sweeps also handles angle measurements and noisy measurements. We demonstrate the practicality of our algorithm through extensive simulations on a large number of networks, upon which it consistently localizes one-thousand-node networks of average degree less than five in less than two minutes on a consumer PC.

Network localization in partially localizable networks

Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., networks in which there exist nodes whose positions cannot be uniquely determined. There is no existing study which correctly identifies precisely which nodes in a network are uniquely localizable and which are not. This absence of a sufficient uniqueness condition permits the computation of erroneous positions that may in turn lead applications to produce flawed results. In this paper, in addition to demonstrating the relevance of networks that may not be fully localizable, we design the first framework for two dimensional network localization with an efficient component to correctly determine which nodes are localizable and which are not. Implementing this system, we conduct comprehensive evaluations of network localizability, providing guidelines for both network design and deployment. Furthermore, we study an integration of traditional geographic routing with geographic routing over virtual coordinates in the partially localizable network setting. We show that this novel cross-layer integration yields good performance, and argue that such optimizations will be likely be necessary to ensure acceptable application performance in partially localizable networks.

On the Computational Complexity of Sensor Network Localization

Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances between all pairs of sensors that are within some radius r of each other. In the past few years, many algorithms for solving the localization problem were proposed, without knowing the computational complexity of the problem. In this paper, we show that no polynomial-time algorithm can solve this problem in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP. We also discuss the consequences of our result and present open problems.

Graphical properties of easily localizable sensor networks

The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of inter-sensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions.