I'm currently planning for my own new story, and in one point in time there will be a city somewhere on the Atlantic Ocean which has to have the space resources necessary to sustain for around 1 billion people, the survivors of a global catastrophe. There is no possibility for people to live elsewhere, as this city (which has no final name yet) is the only safe place. How should the city be designed in terms of housing, growing food, transportation and overall look of the city to support that much people in the smallest volume possible without lowering the live standards below basic levels (everyone has food, water, a place to sleep and some entertainment)?
Assume current technology, or technology which comes likely in the next decade, with a few exceptions: every basic work, including growing food and maintaining every part of the city can be done by robots. You have no energy problems, because if you need more power you build more fusion reactors (which are completely safe in this universe). Also you have super strong and super light building materials, so building structures which are 4 km tall is no problem.
The whole city should be air-locked. There should be no damages or deaths if the city was suddenly transported to a vacuum. So it has to clean it's own air if the atmosphere is not available.
Government is a dictatorship of a single long-living trans-human, which controls every system of the city and cannot be removed. Assume this dictator does only good and will do no harm.
Population can be controlled by contraceptives in the food and water. The inhabitants have no control over this.
The city should not be impacted by tsunamis, storms or freak waves.
There don't have to be enough ships, planes or other means of transport to the land, because leaving the city is not intended.
Water and air have to be cleaned of bacteria and viruses, because there exists very harmful types with could infect the whole city. There exists a 100% reliable test for such pathogens, but no cure, so every infected has to be burned.
PS: Please be gentle, I have been following Worldbuilding SE for quite a while now, but this is my first question :)