We propose efficient distributed algorithms to aid navigation of a user through a geographic area covered by sensors. The sensors sense the level of danger at their locations and we use this information to find a safe path for the user through the sensor field. Traditional distributed navigation algorithms rely upon flooding the whole network with packets to find an optimal safe path. To reduce the communication expense, we introduce the concept of a skeleton graph which is a sparse subset of the true sensor network communication graph. Using skeleton graphs we show that it is possible to find approximate safe paths with much lower communication cost. We give tight theoretical guarantees on the quality of our approximation and by simulation, show the effectiveness of our algorithms in realistic sensor network situations.
 Sensor networks not only have the potential to change the way we use, interact with, and view computers, but also the way we use, interact with, and view the world around us. In order to maximize the effectiveness of sensor networks, one has to identify, examine, understand, and provide solutions for the fundamental problems related to wireless embedded sensor networks. We believe that one of such problems is to determine how well the sensor network monitors the instrumented area. These problems are usually classified as coverage problems. There already exist several methods that have been proposed to evaluate a sensor network's coverage.We start from one of such method and provide a new approach to complement it. The method of using the minimal exposure path to quantify coverage has been optimally solved using a numerical approximation approach. The minimal exposure path can be thought of as the worst-case coverage of a sensor network. Our first goal is to develop an efficient localized algorithm that enables a sensor network to determine its minimal exposure path. The theoretical highlight of this paper is the closed-form solution for minimal exposure in the presence of a single sensor. This solution is the basis for the new and significantly faster localized approximation algorithm that reduces the theoretical complexity of the previous algorithm. On the other hand, we introduce a new coverage problem - the maximal exposure path - which is in a sense the best-case coverage path for a sensor network. We prove that the maximal exposure path problem is NP-hard, and thus, we provide heuristics to generate approximate solutions.In addition, we demonstrate the effectiveness of our algorithms through several simulations. In the case of the minimal single-source minimal exposure path, we use variational calculus to determine exact solutions. For the case of maximal exposure, we use networks with varying numbers of sensors and exposure models. We develop distributed algorithms for self-organizing sensor networks that respond to directing a target through a region. The sensor network models the danger levels sensed across its area and has the ability to adapt to changes. It represents the dangerous areas as obstacles. A protocol that combines the artificial potential field of the sensors with the goal location for the moving object guides the object incrementally across the network to the goal, while maintaining the safest distance to the danger areas. We give the analysis to the protocol and report on hardware experiments using a physical sensor network consisting of Mote sensors. Wireless ad-hoc sensor networks will provide one of the missing connections between the Internet and the physical world. One of the fundamental problems in sensor networks is the calculation of coverage. Exposure is directly related to coverage in that it is a measure of how well an object, moving on an arbitrary path, can be observed by the sensor network over a period of time. In addition to the informal definition, we formally define exposure and study its properties. We have developed an efficient and effective algorithm for exposure calculation in sensor networks, specifically for finding minimal exposure paths. The minimal exposure path provides valuable information about the worst case exposure-based coverage in sensor networks. The algorithm works for any given distribution of sensors, sensor and intensity models, and characteristics of the network. It provides an unbounded level of accuracy as a function of run time and storage. We provide an extensive collection of experimental results and study the scaling behavior of exposure and the proposed algorithm for its calculation. In this paper we investigate efficient strategies for supporting on-demand information dissemination and gathering in large-scale vwireless sensor networks. In particular, we propose a "comb-needle" discovery support model resembling an ancient method: use a comb to help find a needle in sands or a haystack. The model combines push and pull for information dissemination and gathering. The push component features data duplication in a linear neighborhood of each node. The pull component features a dynamic formation of an on-demand routing structure resembling a comb. The comb-needle model enables us to investigate the cost of a spectrum of push and pull combinations for supporting discovery and query in large scale sensor networks. Our result shows that the optimal routing structure depends on the frequency of query occurrence and the spatial-temporal frequency of related events in the network. The benefit of balancing push and pull for discovery in large scale geometric networks are demonstrated. We also raise the issue of query coverage in unreliable networks and investigate how redundancy can improve the coverage via both theoretical analysis and simulation. Last, we study adaptive strategies for the case where the frequencies of query and events are unknown a priori and time-varying. 