OK to extra clarify there are techniques to make the drunken walk more efficient. You might compartmentalize interacting bits into a smaller compartment which scales with the cube of the compartment ratio. You might anchor the participants in an interaction to a membrane, which turns a ~>6 dof search into a ~>3 dof (x, y, rotation) search. You might anchor the participants to a filament or DNA which makes the search a ~> 1 dof search.