Babai-Szemeredi reachability lemma

Statement
Suppose $$G$$ is a finite group and $$S$$ is a generating set for $$G$$. Then, every element $$g \in G$$ can be expressed using a word $$w$$ with letters from $$S$$ such that the straight-line complexity straight-line complexity of $$w$$ is at most $$(1 + \log_2|G|)^2$$.

The technique used in the proof goes by the name of cube doubling.