Most interesting/important algorithms developed in the last decade?
hga: This is not my field, but the hash array mapped trie from 2000-1 (http://en.wikipedia.org/wiki/Hash_array_mapped_trie) is the source of Clojure's "secret sauce" that is its answer to the functional programming trivial update problem.  Updates are O(N) where N is a max of 32 and more likely 5-6, according to Rich Hickey.