Day 2 of SODA, and the tenth time I've been asked "are you chairing all the sessions" ? No, just that many of my PC colleagues didn't (or couldn't) show up :), so those of us who did are doing more lifting. In reward, we got a nice dinner in the French quarter, and I tasted boudin for the first time (and maybe the last).
An interesting talk today morning by Dror Aiger on reporting near neighbors. They were able to show a not-super-exponential relation between the number of points at unit $\ell_\infty$ distance from a query, and the number of points at unit $\ell_2$ distance. This was wrapped into a fast algorithm for reporting Euclidean near neighbors in high dimensions that has some interesting (if preliminary) experimental backing as well in comparison with ANN, FLANN and LSH.
Jan Vondrák gave the invited talk on submodular optimization. I mentioned Satoru Fujishige's talk at NIPS, and this was an excellent complement. Fujishige's talk focused on the geometric intuition behind submodular functions (especially the associated polymatroid). Vondrák's talk focused on the algorithmic implications of submodularity, and he gave very convincing arguments for why it can be viewed as discrete convexity OR discrete concavity, or even neither. He pointed out how the Lovasz extension is useful for minimization and the multilinear extension is more useful for maximization, and gave a number of "recipes" for designing algorithms that optimize submodular functions. I hope the slides go online at some point: they were very clear and well-balanced.
There was some discussion over whether next year's SODA should adopt the two-tier PC that STOC is currently experimenting. The jury's still out on that, and since the STOC PC is not done with their work, we don't yet have formal feedback. I will admit to being a little frustrated with the level of conservativeness on display here: it's not as if EVERY OTHER COMMUNITY IN CS doesn't do this and doesn't have best practices that we can learn from, and given our reviewing loads, it's really crazy that we aren't desperately trying things to alleviate the problem.