The Gale-Shapley algorithm provides a stable, orderly way to match pairs, much like we create chains for kidney swaps where a donor and recipient are incompatible but can find a match in another pair. It prevents unstable matches where a donor and recipient might later abandon the chain for a better option. In our registry, this logic helps build longer, life-saving chains across cities. I know this because I've seen the relief on a father's face in Delhi when we told him his daughter's donor in Chennai was found through such a calculated chain—it turns despair into a precise map of hope.
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