According to the link, it's O(n^3) if certain simplifying assumptions are made. (Said simplifying assumptions include that returns to scale are never positive - which isn't too unrealistic when you're talking about the difference between making a million diapers or a million plus one of diapers, but is unrealistic as hell when you're talking about intellectual property or anything with large R&D costs.) However, the same conditions under which central planning actually becomes harder than O(n^3) are the same conditions under which the market allocation is inefficient, too - they're the same kinds of conditions that tend to create monopolies, tragedy of the commons situations, etc.
Moved to open thread, since my point turned more general than just a response.
Three Toed Sloth has a nice exposition on the difficulties of optimizing an economy, including the best explanation of convex optimization ever: