Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition. When my students first saw this title they were sure it had been caused by a spellchecker run amok, and they spent some time and amusement trying to figure out what "pants" really means. It's really pants, and I don't mean the British slang for "bad": a pair of pants is a topological surface with three boundary curves. I'd copy the abstract here but it's only a link away. It's on approximation algorithms for hierarchical clustering, with various definitions of what it means to be a good clustering, anyway.

This is the paper for which I needed the entropy inequality that I was discussing here a while back. The inequality comes up in proving the approximation ratio for one of the problems, in that my algorithm has solution quality upper bounded by one kind of entropy and the problem has solution quality lower bounded by the other kind of entropy.

I also have slides from a departmental seminar on the same results available. They used to be dry and technical but Mike Goodrich persuaded me to add some clip art of Spongebob. So now they're dry and technical with a thin veneer of cartoon humor on top.

ETA: Jeff finds some prior art