Curiosities · Foundation · 11 min
Moving things efficiently
Optimal transport moves the right amount of mass while minimizing total cost.
WHAT HAPPENS IF…For p=0.75 and q=0.25, what is the minimum cost?
Loading the mathematical model…
Sources place masses p and 1−p at 0 and 2; targets place q and 1−q at 1 and 3. Ordered matching sends the leftmost remaining mass to the leftmost unmet target. When p>q, the excess p−q travels distance 3 instead of 1, adding 2(p−q) to the baseline cost 1. This result is specific to one-dimensional absolute-distance cost.
A detail that matters
Choosing the globally nearest pair first is not a valid general transport algorithm.
Keep the connection going
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