Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is 2-connected 1 . The problem is NP -hard. In this paper we develop O(1)-approximation algorithms that find close to optimal solutions in time O((kn) 2 ) for achieving k-edge connectivity of n nodes. The worst case approximation guarantee is 10, but the algorithm produces solutions that are far better than this bound suggests. We also consider extensions to higher dimensions, and the scheme that we develop for points in the plane, yields a bound of 2d MST where dMST is the maximum degree of a minimum-degree Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles).We also prove that if the sensors are uniformly and identically distributed in a unit square, the expected number of relay nodes required goes to zero as the number of sensors goes to infinity.

Abstract-In this paper we introduce a novel approach for the routing problem in wireless ad hoc networks. Our approach is based on the analogy of the routing problem to the distribution of electric field in a physical media with a given density of charges. We show that the throughput can be significantly increased by choosing routes in such a way that the traffic is spread as uniformly as possible throughout the network. Achieving this uniform spreading requires solution of a set of partial differential equations similar to Maxwell's equations in the electrostatic theory. While the main focus in the paper is on the case in which many sources communicate with a single destination, extension to the case of multiple destinations is also described.

No abstract

No abstract

ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical,heterogeneous and dynamic problems of engineering technology and systems for industry and government.