I have a class, let's say Person, which is managed by another class/module, let's say PersonPool.
I have another module in my application, let's say module M, that wants to associate information with a person, in the most efficient way. I considered the following alternatives:
In the last alternative, the problem could be solved by using a sparse vector, but I don't know if there are very efficient implementations of a sparse vector (faster than a map/hashmap).
Are there other ways of getting this done? Or is there an efficient sparse vector that might solve the memory problem of the last alternative?
The first and third are reasonably common techniques. The second is how dynamic programming languages such as Python and Javascript implement member data for objects, so do not dismiss it out of hand as impossibly slow. The fourth is in the same ballpark as how relational databases work. It is possible, but difficult, to make relational databases run the like the clappers.
In short, you've described 4 widely used techniques. The only way to rule any of them out is with details specific to your problem (required performance, number of Persons, number of properties, number of modules in your code that will want to do this, etc), and corresponding measurements.
Another possibility is for module M to define a class which inherits from Person, and adds extra data members. The principle here is that M's idea of a person differs from Person's idea of a person, so describe M's idea as a class. Of course this only works if all other modules operating on the same Person objects are doing so via polymorphism, and furthermore if M can be made responsible for creating the objects (perhaps via dependency injection of a factory). That's quite a big "if". An even bigger one, if nothing other than M needs to do anything life-cycle-ish with the objects, then you may be able to use composition or private inheritance in preference to public inheritance. But none of it is any use if module N is going to create a collection of Persons, and then module M wants to attach extra data to them.