Can Divorces Lead to a Happy Ending in Marriage?

Ever thought about how to fix a bad marriage? Well, let's talk about a puzzle called "Reaching Stable Marriage via Divorces" or DivorceSM for short. This riddle asks if you can start with a not-so-great marriage match and end up with a stable one by just allowing divorces. You see, stable marriages are like those fairytale endings where everyone is happy. But getting there can be tough, especially if you start with a bad match. Researchers have been trying to figure out if you can use divorces to fix things.

It turns out, for marriages where people have clear preferences (no ties), finding a stable match through divorces is really hard. Like, NP-hard hard. That means it's a puzzle that's tough to solve, even for computers. Even if you limit the number of divorce operations or keep the preference lists short, it stays hard. But, if you look at both the number of divorces and the length of preference lists together, it becomes a bit easier. So, while divorces can help, they might not always lead to that happy ending. It's like trying to solve a really complex puzzle.

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