Introduction

We will continue leveraging the skills acquired in the first two modules, revising many of the concepts. This time our context is from telecommunications: how to place wireless antennas (such as cellphone towers), assuming a simplified mathematical model --- the town is a flat square and each antenna has a circular range of the same radius. We will delve deeper into the concept of optimization: how do the decisions we make affect things such as cost and quality?

Learning outcomes

This module will help you do the following:

• Do rejection sampling (Monte Carlo method: accept pseudorandom data that meets a certain condition)
• Quantify the consequences of our choices (total coverage of possibly overlapping antennas)
• avoid symbolic mathematics by applying simple computation (think in terms of pixels instead of pigeon-hole principles)
• Normalize values to the unit interval (i.e., make many numbers be from zero to one while maintaining their relative magnitudes)
• Identify alternative ways to arrive at the same result and pick the one that requires fewer calculations
• Work with two contradictory objectives simultaneously (maximize coverage, minimize the antenna count)

Warm-up

Warm-up assessment

Write down some ideas that you have regarding how to determine the placement of each sensor node in a wireless sensor network. Concentrate on things such as connectivity between the components so as to allow communication and the cost of the setup as a whole in terms of how many nodes you would need to position to adequately monitor a fixed area.

Concepts

After this module, you should be familiar with the following concepts:

• Maximization
• Coverage
• Proportion
• Normalization
• Bi-objective

Remember that you can always look concepts up in the glossary. Should anything be missing or insufficient, please report it.