The motivating application for this problem is the channel assignment problem. The
frequency of a transmitting radio station may interfere with frequencies of neighboring
radio stations. Similar interference may occur in cell phone networks and other radio
transmitting networks. We therefore need to find the most efficient way to assign
non-

Wireless sensor networks (WSNs) are an exciting new technology that lies at the intersection
of communication networks and smart monitoring. It is easy to imagine the benefits
of a system consisting of hundreds or even thousands of sensors distributed over
a region or an object and able to measure any of a multitude of aspects of their
environment, before passing the information to a central base station for intelligent
processing. The applications are countless: early detection of bushfires, smart-

Although WSNs are already extensively utilised in the real world, their full potential
remains largely untapped. In contrast to other types of communication networks, sensor
network technology is fundamentally constrained by existing battery technology and
energy conservation protocols. This is because WSNs are required to be autonomous
for as long as possible, as they are often deployed in remote, harsh, or even hostile
environments.

The topology of a WSN, which is the overall pattern formed by the communication links between pairs of sensors, and the relative locations of the sensors within the sensing field, play a large role in the efficiency of the network. This project therefore aims to optimise the topological design and sensor location phase of repairing (augmenting) or deploying a WSN. The project focuses on all of the following design stages: the development of mathematical tools to model and understand optimal WSN deployments and augmentations, the application of these tools to the construction of new algorithms, and the performance analysis of algorithms by mathematical means and by coding the algorithms and performing simulations.

Survivable networks continue to function after the failure of multiple links (edges)
or nodes. The survivable network problem requires the construction of “low-

There are two main classes of problem:

1) The graph problem, where a weighted graph is given and one must find a survivable spanning subgraph of minimum cost. Popular methods for solving this problem are based on integer programming and polyhedral theory,

2) The geometric problem, where nodes have coordinates but not all node locations
are given. An ambient geometric space or norm is specified, and the locations of
at least some of the nodes (the so-

Given a set of points in a normed space, draw a set of straight line segments so that the resultant set is connected, contains all given points, and is of minimum total length. This is also known as the Steiner tree problem, especially when the norm is Euclidean or rectilinear.

Proximity graphs are geometric graphs like Voronoi diagrams and Gabriel graphs that are defined by certain “closeness” relations between points in a given set. These graphs have extensive applications, including network design, telecommunications, robotics, computer graphics, cartography, and data analysis.

Example: Beta-