An Analytical Expression for k-connectivity of Wireless Ad Hoc Networks

Over the last few years coverage and connectivity of wireless ad hoc networks have fascinated considerable attention. The presented paper analyses and investigates the issues of k-connectivity probability and its robustness in wireless ad hoc-network while considering fading techniques like lognormal fading, Rayleigh fading, and nakagami fading in the ad hoc communication environment, by means of shadowing and fading phenomenon. In case of k-connected wireless sensor network (WSNs), this technique permits the routing of data packets or messages via individual (one or more) of minimum k node disjoint communication paths, but the other remaining paths can also be used. The major contribution of the paper is mathematical expressions for k-connectivity probability

Reliably Detecting Connectivity using Local Graph Traits

Local distributed algorithms can only gather sufficient information to identify local graph traits, that is, properties that hold within the local neighborhood of each node. However, it is frequently the case that global graph properties (connectivity, diameter, girth, etc) have a large influence on the execution of a distributed algorithm. This paper studies local graph traits and their relationship with global graph properties. Specifically, we focus on graph k-connectivity. First we prove a negative result that shows there does not exist a local graph trait which perfectly captures graph k-connectivity. We then present three different local graph traits which can be used to reliably predict the k-connectivity of a graph with varying degrees of accuracy. As a simple application of these results, we present upper and lower bounds for a local distributed algorithm which determines if a graph is k-connected. As a more elaborate application of local graph traits, we describe, and prove the correctness of, a local distributed algorithm that preserves k-connectivity in mobile ad hoc networks while allowing nodes to move independently whenever possible

Cross-Layer Resilience Based On Critical Points in MANETs

A fundamental problem in mobile ad hoc and unstructured sensor networks is maintaining connectivity. A network is connected if all nodes have a communication route (typically multi-hop) to each other. Maintaining connectivity is a challenge due to the unstructured nature of the network topology and the frequent occurrence of link and node failures due to interference, mobility, radio channel effects and battery limitations. In order to effectively deploy techniques to improve the resilience of sensor and mobile ad hoc networks against failures or attacks one must be able to identify all the weak points of a network topology. Here we define the weak or critical points of the topology as those links and nodes whose failure results in partitioning of the network. In this dissertation, we propose a set of algorithms to identify the critical points of a network topology. Utilizing these algorithms we study the behavior of critical points and the effect of using only local information in identifying global critical points. Then, we propose both local and global based resilient techniques that can improve the wireless network connectivity around critical points to lessen their importance and improve the network resilience. Next we extend the work to examine the network connectivity for heterogeneous wireless networks that can be result due to factors such as variations in transmission power and signal propagation environments and propose an algorithm to identify the connectivity of the network. We also propose two schemes for constructing additional links to enhance the connectivity of the network and evaluate the network performance of when a random interference factor occurs. Lastly, we implement our resilience techniques to improve the performance

Local distributed algorithms for multi-robot systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 165-173) and index.The field of swarm robotics focuses on controlling large populations of simple robots to accomplish tasks more effectively than what is possible using a single robot. This thesis develops distributed algorithms tailored for multi-robot systems with large populations. Specifically we focus on local distributed algorithms since their performance depends primarily on local parameters on the system and are guaranteed to scale with the number of robots in the system. The first part of this thesis considers and solves the problem of finding a trajectory for each robot which is guaranteed to preserve the connectivity of the communication graph, and when feasible it also guarantees the robots advanced towards a goal defined by an arbitrary motion planner. We also describe how to extend our proposed approach to preserve the k-connectivity of a communication graph. Finally, we show how our connectivity-preserving algorithm can be combined with standard averaging procedures to yield a provably correct flocking algorithm. The second part of this thesis considers and solves the problem of having each robot localize an arbitrary subset of robots in a multi-robot system relying only on sensors at each robot that measure the angle, relative to the orientation of each robot, towards neighboring robots in the communication graph. We propose a distributed localization algorithm that computes the relative orientations and relative positions, up to scale, of an arbitrary subset of robots. For the case when the robots move in between rounds we show how to use odometry information to allow each robot to compute the relative positions complete with scale, of an arbitrary subset of robots. Finally we describe how to use the our localization algorithm to design a variety of multi-robot tasks.by Alejandro Cornejo.Ph.D