AKA "static memory allocation", since the heights of the rectangles can be interpreted as buffer sizes, and their widths as lifetimes.
Most of my PhD's effort has been devoted to beating the SOTA in this. Problem's importance nowadays is owed to deep learning's memory wall.
http://adambuchsbaum.com/papers/dsa-stoc03.pdf
https://link.springer.com/chapter/10.1007/978-3-540-27798-9_...
https://users.cs.northwestern.edu/~pdinda/ics-s05/doc/dsa.pd...
there are also some from ML people trying to allocate memory optimally for DNNs:
https://arxiv.org/abs/1907.01989
https://arxiv.org/abs/1804.10001
https://arxiv.org/abs/2001.03288
they all boil down to a couple of greedy heuristics. the most recent "cool" paper was from a group at google
https://dl.acm.org/doi/10.1145/3567955.3567961
basic idea is to use both ILP and heurstics. i asked them to open source but no dice :(