Android :: Determine Phone's Proximity To Known Point While Conserving Power

I am trying to determine if an Android user has had a close proximity to a list of predetermined locations. I'd like to do this with the least amount of drain on the phone's battery. The two mechanisms I see for accomplishing this are proximity alerts and requesting location updates. What are the pros and cons of the two methods? Will one have less affect on the battery than the other? In either case I would guess the specific location manager used would have some affect power usage (existing Stack Overflow answer).