I am looking for a book about an extremely overpopulated world where caring was a liability. It's a love story of how these two people manage to care for each other in that world. It's also about ruthlessness really. I'm trying to find the author and/or the title. There were also outsiders that weren't part of the main system that was featured somehow. I think it was so overpopulated that they had to sleep in shifts.
This sounds like Philip Jose Farmer's noted short story "The Sliced-Crosswise Only-On-Tuesday World", which he later used as the inspiration for his "Dayworld" series. Both are about a future in which everyone sleeps in stasis except one day a week as a solution to overpopulation. The original short story is a thwarted romance between two people who live on different days. I don't remember reading the novel, but according to Wikipedia it features a group of outsiders trying to change the system.