The shortest length of campaign that you can run will vary greatly based on the medium chosen.
Digital outdoor advertising campaigns can be compressed into whatever timeline is necessary while traditional outdoor media requires longer. Outdoor media has been sold in 4-week periods for 100+ years but this is evolving quickly as traditional media locations are being converted to digital in all major markets.
Don’t forget about production costs, which make shorter traditional outdoor campaigns much more expensive. If you amortize production costs over a longer campaign, it stings a bit less.